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Isometry group of Lorentz manifolds: A coarse perspective Geom. Funct. Anal. (IF 2.148) Pub Date : 20211130
Frances, CharlesWe prove a structure theorem for the isometry group \({\text {Iso}}(M,g)\) of a compact Lorentz manifold, under the assumption that a closed subgroup has exponential growth. We don’t assume anything about the identity component of \({\text {Iso}}(M,g)\), so that our results apply for discrete isometry groups. We infer a full classification of lattices that can act isometrically on compact Lorentz manifolds

Singularity of discrete random matrices Geom. Funct. Anal. (IF 2.148) Pub Date : 20211022
Jain, Vishesh, Sah, Ashwin, Sawhney, MehtaabLet \(\xi \) be a nonconstant realvalued random variable with finite support and let \(M_{n}(\xi )\) denote an \(n\times n\) random matrix with entries that are independent copies of \(\xi \). For \(\xi \) which is not uniform on its support, we show that $$\begin{aligned} {\mathbb {P}}[M_{n}(\xi )\text { is singular}]&= {\mathbb {P}}[\text {zero row or column}] \\ {}&\quad +(1+o_n(1)){\mathbb {P}}[\text

The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions Geom. Funct. Anal. (IF 2.148) Pub Date : 20211020
Logunov, A., Malinnikova, E., Nadirashvili, N., Nazarov, F.Let \(\Omega \) be a bounded domain in \({\mathbb {R}}^n\) with \(C^{1}\) boundary and let \(u_\lambda \) be a Dirichlet Laplace eigenfunction in \(\Omega \) with eigenvalue \(\lambda \). We show that the \((n1)\)dimensional Hausdorff measure of the zero set of \(u_\lambda \) does not exceed \(C(\Omega )\sqrt{\lambda }\). This result is new even for the case of domains with \(C^\infty \)smooth boundary

Uniformization of compact complex manifolds by Anosov homomorphisms Geom. Funct. Anal. (IF 2.148) Pub Date : 20210914
Dumas, David, Sanders, AndrewWe study uniformization problems for compact manifolds that arise as quotients of domains in complex flag varieties by images of Anosov homomorphisms. We focus on Anosov homomorphisms with “small” limit sets, as measured by the Riemannian Hausdorff codimension in the flag variety. Under such a codimension hypothesis, we show that all firstorder deformations of complex structure on the associated compact

A proof of Ringel’s conjecture Geom. Funct. Anal. (IF 2.148) Pub Date : 20210902
Montgomery, R., Pokrovskiy, A., Sudakov, B.A typical decomposition question asks whether the edges of some graph G can be partitioned into disjoint copies of another graph H. One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edgedisjoint copies of a tree. It says that any tree with n edges packs \(2n+1\) times into the complete graph \(K_{2n+1}\). In this

A numerical criterion for generalised MongeAmpère equations on projective manifolds Geom. Funct. Anal. (IF 2.148) Pub Date : 20210901
Datar, Ved V., Pingali, Vamsi PrithamWe prove that generalised MongeAmpère equations (a family of equations which includes the inverse Hessian equations like the Jequation, as well as the MongeAmpère equation) on projective manifolds have smooth solutions if certain intersection numbers are positive. As corollaries of our work, we improve a result of Chen (albeit in the projective case) on the existence of solutions to the Jequation

Sweepouts of closed Riemannian manifolds Geom. Funct. Anal. (IF 2.148) Pub Date : 20210831
Nabutovsky, Alexander, Rotman, Regina, Sabourau, StéphaneWe show that for every closed Riemannian manifold there exists a continuous family of 1cycles (defined as finite collections of disjoint closed curves) parametrized by a sphere and sweeping out the whole manifold so that the lengths of all connected closed curves are bounded in terms of the volume (or the diameter) and the dimension n of the manifold, when \(n \ge 3\). An alternative form of this

Monodromy groups of Kloosterman and hypergeometric sheaves Geom. Funct. Anal. (IF 2.148) Pub Date : 20210829
Katz, Nicholas M., Tiep, Pham HuuWe study the possible structures of monodromy groups of Kloosterman and hypergeometric sheaves on \({{\mathbb {G}}}_m\) in characteristic p. We show that most such sheaves satisfy a certain condition \(\mathrm {(\mathbf{S+})}\), which has very strong consequences on their monodromy groups. We also classify the finite, almost quasisimple, groups that can occur as monodromy groups of Kloosterman and

Conformal upper bounds for the volume spectrum Geom. Funct. Anal. (IF 2.148) Pub Date : 20210824
Wang, ZhichaoIn this paper, we prove upper bounds for the volume spectrum of a Riemannian manifold that depend only on the volume, dimension and a conformal invariant.

Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems Geom. Funct. Anal. (IF 2.148) Pub Date : 20210813
Girouard, Alexandre, Karpukhin, Mikhail, Lagacé, JeanWe associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and other classical eigenvalue problems. In the first part of the paper we study the properties of variational eigenvalues and establish a general continuity result, which shows for a sequence of measures converging in the dual

Generic scarring for minimal hypersurfaces along stable hypersurfaces Geom. Funct. Anal. (IF 2.148) Pub Date : 20210702
Antoine Song, Xin ZhouLet \(M^{n+1}\) be a closed manifold of dimension \(3\le n+1\le 7\). We show that for a \(C^\infty \)generic metric g on M, to any connected, closed, embedded, 2sided, stable, minimal hypersurface \(S\subset (M,g)\) corresponds a sequence of closed, embedded, minimal hypersurfaces \(\{\Sigma _k\}\) scarring along S, in the sense that the area and Morse index of \(\Sigma _k\) both diverge to infinity

Local uniformity through larger scales Geom. Funct. Anal. (IF 2.148) Pub Date : 20210630
Miguel N. WalshBy associating frequencies to larger scales, we provide a simpler way to derive local uniformity of multiplicative functions on average from the results of MatomäkiRadziwiłł.

Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves Geom. Funct. Anal. (IF 2.148) Pub Date : 20210618
S. Yu. OrevkovWe prove two inequalities for the complex orientations of a separating nonsingular real algebraic curve in \({\mathbb {RP}}^2\) of any odd degree. We also construct a separating nonsingular real (i.e., invariant under the complex conjugation) pseudoholomorphic curve in \({\mathbb {CP}}^2\) of any degree congruent to 9 mod 12 which does not satisfy one of these inequalities. Therefore the oriented

Building manifolds from quantum codes Geom. Funct. Anal. (IF 2.148) Pub Date : 20210618
Michael Freedman, Matthew HastingsWe give a procedure for “reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex over \({\mathbb {Z}}\). Applying this procedure to chain complexes obtained by “lifting" recently developed quantum codes, which correspond to chain complexes over \({\mathbb {Z}}_2\), we construct the first examples of power law \({\mathbb {Z}}_2\) systolic

Deformations of Totally Geodesic Foliations and Minimal Surfaces in Negatively Curved 3Manifolds Geom. Funct. Anal. (IF 2.148) Pub Date : 20210602
Ben LoweLet \(g_t\) be a smooth 1parameter family of negatively curved metrics on a closed hyperbolic 3manifold M starting at the hyperbolic metric. We construct foliations of the Grassmann bundle \(Gr_2(M)\) of tangent 2planes whose leaves are (lifts of) minimal surfaces in \((M,g_t)\). These foliations are deformations of the foliation of \(Gr_2(M)\) by (lifts of) totally geodesic planes projected down

Entangleability of cones Geom. Funct. Anal. (IF 2.148) Pub Date : 20210515
Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos, Martin PlávalaWe solve a longstanding conjecture by Barker, proving that the minimal and maximal tensor products of two finitedimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Here, given two proper cones \({\mathcal {C}}_1\), \({\mathcal {C}}_2\), their minimal tensor product is the cone generated by products of the form \(x_1\otimes x_2\), where

Nonasymptotic Results for Singular Values of Gaussian Matrix Products Geom. Funct. Anal. (IF 2.148) Pub Date : 20210508
Boris Hanin, Grigoris PaourisThis article provides a nonasymptotic analysis of the singular values (and Lyapunov exponents) of Gaussian matrix products in the regime where N, the number of terms in the product, is large and n, the size of the matrices, may be large or small and may depend on N. We obtain concentration estimates for sums of Lyapunov exponents, a quantitative rate for convergence of the empirical measure of the

Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition Geom. Funct. Anal. (IF 2.148) Pub Date : 20210508
Steve Hofmann, José María Martell, Svitlana Mayboroda, Tatiana Toro, Zihui ZhaoThe present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic measure with respect to the surface measure and uniform rectifiability of the boundary are equivalent, in an optimal class of divergence form elliptic operators satisfying

Flows on measurable spaces Geom. Funct. Anal. (IF 2.148) Pub Date : 20210508
László LovászThe theory of graph limits is only understood to a somewhat satisfactory degree in the cases of dense graphs and of bounded degree graphs. There is, however, a lot of interest in the intermediate cases. It appears that one of the most important constituents of graph limits in the general case will be Markov spaces (Markov chains on measurable spaces with a stationary distribution). This motivates our

A pair correlation problem, and counting lattice points with the zeta function Geom. Funct. Anal. (IF 2.148) Pub Date : 20210508
Christoph Aistleitner, Daniel ElBaz, Marc MunschThe pair correlation is a localized statistic for sequences in the unit interval. Pseudorandom behavior with respect to this statistic is called Poissonian behavior. The metric theory of pair correlations of sequences of the form \((a_n \alpha )_{n \ge 1}\) has been pioneered by Rudnick, Sarnak and Zaharescu. Here \(\alpha \) is a real parameter, and \((a_n)_{n \ge 1}\) is an integer sequence, often

The Novikov conjecture, the group of volume preserving diffeomorphisms and HilbertHadamard spaces Geom. Funct. Anal. (IF 2.148) Pub Date : 20210410
Sherry Gong, Jianchao Wu, Guoliang YuWe prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible HilbertHadamard space. Admissible HilbertHadamard spaces are a class of (possibly infinitedimensional) nonpositively curved metric spaces that contain dense sequences of closed convex subsets isometric to Riemannian manifolds. Examples of admissible HilbertHadamard

Nondisplaceable Lagrangian links in fourmanifolds Geom. Funct. Anal. (IF 2.148) Pub Date : 20210408
Cheuk Yu Mak, Ivan SmithLet \(\omega \) denote an area form on \(S^2\). Consider the closed symplectic 4manifold \(M=(S^2\times S^2, A\omega \oplus a \omega )\) with \(0

Short geodesic loops and $$L^p$$ L p norms of eigenfunctions on large genus random surfaces Geom. Funct. Anal. (IF 2.148) Pub Date : 20210405
Clifford Gilmore, Etienne Le Masson, Tuomas Sahlsten, Joe ThomasWe give upper bounds for \(L^p\) norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces in terms of a parameter depending on the growth rate of the number of short geodesic loops passing through a point. When the genus \(g \rightarrow +\infty \), we show that random hyperbolic surfaces X with respect to the WeilPetersson volume have with high probability at most one such loop of length

Simultaneous Small Fractional Parts of Polynomials Geom. Funct. Anal. (IF 2.148) Pub Date : 20210401
James MaynardLet \(f_1,\dots ,f_k\in \mathbb {R}[X]\) be polynomials of degree at most d with \(f_1(0)=\dots =f_k(0)=0\). We show that there is an \(n

On the variance of squarefree integers in short intervals and arithmetic progressions Geom. Funct. Anal. (IF 2.148) Pub Date : 20210331
Ofir Gorodetsky, Kaisa Matomäki, Maksym Radziwiłł, Brad RodgersWe evaluate asymptotically the variance of the number of squarefree integers up to x in short intervals of length \(H < x^{6/11  \varepsilon }\) and the variance of the number of squarefree integers up to x in arithmetic progressions modulo q with \(q > x^{5/11 + \varepsilon }\). On the assumption of respectively the Lindelöf Hypothesis and the Generalized Lindelöf Hypothesis we show that these ranges

An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture Geom. Funct. Anal. (IF 2.148) Pub Date : 20210324
Yuansi ChenWe prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency \(d^{o_d(1)}\). When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency \(d^{1/4}\). Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many

$$\mathbf {Bad}\left( {\mathbf {w}}\right) $$ Bad w is hyperplane absolute winning Geom. Funct. Anal. (IF 2.148) Pub Date : 20210313
Victor Beresnevich, Erez Nesharim, Lei YangIn 1998 Kleinbock conjectured that any set of weighted badly approximable \(d\times n\) real matrices is a winning subset in the sense of Schmidt’s game. In this paper we prove this conjecture in full for vectors in \({\mathbb {R}}^d\) in arbitrary dimensions by showing that the corresponding set of weighted badly approximable vectors is hyperplane absolute winning. The proof uses the Cantor potential

A landing theorem for entire functions with bounded postsingular sets Geom. Funct. Anal. (IF 2.148) Pub Date : 20201120
Anna Miriam Benini, Lasse RempeThe DouadyHubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial f with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue

DistributionValued Ricci Bounds for Metric Measure Spaces, Singular Time Changes, and Gradient Estimates for Neumann Heat Flows Geom. Funct. Anal. (IF 2.148) Pub Date : 20201120
KarlTheodor SturmWe will study metric measure spaces \((X,\mathsf{d},{\mathfrak {m}})\) beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distributionvalued lower Ricci bounds \(\mathsf{BE}_1(\kappa ,\infty )\) for which we prove the equivalence with sharp gradient estimates, the class of which will be preserved under time changes with arbitrary \(\psi \in \mathrm {Lip}_b(X)\)

Classical Theta Lifts for Higher Metaplectic Covering Groups Geom. Funct. Anal. (IF 2.148) Pub Date : 20201118
Solomon Friedberg, David GinzburgThe classical theta correspondence establishes a relationship between automorphic representations on special orthogonal groups and automorphic representations on symplectic groups or their double covers. This correspondence is achieved by using as integral kernel a theta series on the metaplectic double cover of a symplectic group that is constructed from the Weil representation. There is also an analogous

Partial associativity and rough approximate groups Geom. Funct. Anal. (IF 2.148) Pub Date : 20201108
W. T. Gowers, J. LongSuppose that a binary operation \(\circ \) on a finite set X is injective in each variable separately and also associative. It is easy to prove that \((X,\circ )\) must be a group. In this paper we examine what happens if one knows only that a positive proportion of the triples \((x,y,z)\in X^3\) satisfy the equation \(x\circ (y\circ z)=(x\circ y)\circ z\). Other results in additive combinatorics would

Cohomological obstructions to lifting properties for full C $$^*$$ ∗ algebras of property (T) groups Geom. Funct. Anal. (IF 2.148) Pub Date : 20201026
Adrian Ioana, Pieter Spaas, Matthew WiersmaWe develop a new method, based on nonvanishing of second cohomology groups, for proving the failure of lifting properties for full C\(^*\)algebras of countable groups with (relative) property (T). We derive that the full C\(^*\)algebras of the groups \(\mathbb {Z}^2\times \text {SL}_2({\mathbb {Z}})\) and \(\text {SL}_n({\mathbb {Z}})\), for \(n\ge 3\), do not have the local lifting property (LLP)

Regularity of area minimizing currents mod p Geom. Funct. Anal. (IF 2.148) Pub Date : 20201030
Camillo De Lellis, Jonas Hirsch, Andrea Marchese, Salvatore StuvardWe establish a first general partial regularity theorem for area minimizing currents \({\mathrm{mod}}(p)\), for every p, in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an mdimensional area minimizing current \({\mathrm{mod}}(p)\) cannot be larger than \(m1\). Additionally, we show that, when p is odd, the interior singular set

Entropy rigidity for 3D conservative Anosov flows and dispersing billiards Geom. Funct. Anal. (IF 2.148) Pub Date : 20201026
Jacopo De Simoi, Martin Leguil, Kurt Vinhage, Yun YangGiven an integer \(k \ge 5\), and a \(C^k\) Anosov flow \(\Phi \) on some compact connected 3manifold preserving a smooth volume, we show that the measure of maximal entropy is the volume measure if and only if \(\Phi \) is \(C^{k\varepsilon }\)conjugate to an algebraic flow, for \(\varepsilon >0\) arbitrarily small. Moreover, in the case of dispersing billiards, we show that if the measure of maximal

Contractible, hyperbolic but nonCAT(0) complexes Geom. Funct. Anal. (IF 2.148) Pub Date : 20201026
Richard C. H. WebbWe prove that almost all arc complexes do not admit a CAT(0) metric with finitely many shapes, in particular any finiteindex subgroup of the mapping class group does not preserve such a metric on the arc complex. We also show the analogous statement for all but finitely many disc complexes of handlebodies and free splitting complexes of free groups. The obstruction is combinatorial. These complexes

Arithmetic version of Anderson localization via reducibility Geom. Funct. Anal. (IF 2.148) Pub Date : 20201001
Lingrui Ge, Jiangong YouThe arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya (Ann Math 150:1159–1175, 1999) for the almost Mathieu operators (AMO). Later, the result was generalized by Bourgain and Jitomirskaya (Invent Math 148:453–463, 2002) to a class of one dimensional quasiperiodic

A long neck principle for Riemannian spin manifolds with positive scalar curvature Geom. Funct. Anal. (IF 2.148) Pub Date : 20200922
Simone CecchiniWe develop index theory on compact Riemannian spin manifolds with boundary in the case when the topological information is encoded by bundles which are supported away from the boundary. As a first application, we establish a “long neck principle” for a compact Riemannian spin nmanifold with boundary X, stating that if \({{\,\mathrm{scal}\,}}(X)\ge n(n1)\) and there is a nonzero degree map into the

Uniqueness of some Calabi–Yau metrics on $${\mathbf {C}}^{{n}}$$ C n Geom. Funct. Anal. (IF 2.148) Pub Date : 20200907
Gábor SzékelyhidiWe consider the Calabi–Yau metrics on \(\mathbf {C}^n\) constructed recently by Yang Li, Conlon–Rochon, and the author, that have tangent cone \(\mathbf {C}\times A_1\) at infinity for the \((n1)\)dimensional Stenzel cone \(A_1\). We show that up to scaling and isometry this Calabi–Yau metric on \(\mathbf {C}^n\) is unique. We also discuss possible generalizations to other manifolds and tangent cones

Towards a Proof of the FourierEntropy Conjecture? Geom. Funct. Anal. (IF 2.148) Pub Date : 20200905
Esty Kelman, Guy Kindler, Noam Lifshitz, Dor Minzer, Muli SafraThe total influence of a function is a central notion in analysis of Boolean functions, and characterizing functions that have small total influence is one of the most fundamental questions associated with it. The KKL theorem and the Friedgut junta theorem give a strong characterization of such functions whenever the bound on the total influence is \(o(\log n)\). However, both results become useless

Properties of High Rank Subvarieties of Affine Spaces Geom. Funct. Anal. (IF 2.148) Pub Date : 20200820
David Kazhdan, Tamar ZieglerWe use tools of additive combinatorics for the study of subvarieties defined by high rank families of polynomials in high dimensional \({\mathbb {F}}_q\)vector spaces. In the first, analytic part of the paper we prove a number properties of high rank systems of polynomials. In the second, we use these properties to deduce results in Algebraic Geometry , such as an effective Stillman conjecture over

Branching Geodesics in SubRiemannian Geometry Geom. Funct. Anal. (IF 2.148) Pub Date : 20200809
Thomas Mietton, Luca RizziIn this note, we show that subRiemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a nonzero time, which in particular for a strictly normal geodesic means that it contains a nontrivial abnormal subsegment. The simplest example is obtained by gluing the threedimensional Martinet flat structure

Small cap decouplings Geom. Funct. Anal. (IF 2.148) Pub Date : 20200806
Ciprian Demeter, Larry Guth, Hong WangWe develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small cap decoupling for the parabola. Then we find sharp estimates for exponential sums with small frequency separation on the moment curve in \(\mathbb {R}^3\). This

The Infinitesimal Characters of Discrete Series for Real Spherical Spaces Geom. Funct. Anal. (IF 2.148) Pub Date : 20200804
Bernhard Krötz, Job J. Kuit, Eric M. Opdam, Henrik SchlichtkrullLet \(Z=G/H\) be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of G on \(L^2(Z)\). It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of \(L^2(Z)\), have infinitesimal characters which are real and belong to a lattice. Moreover, let K be a maximal compact subgroup

Edge rigidity and universality of random regular graphs of intermediate degree Geom. Funct. Anal. (IF 2.148) Pub Date : 20200717
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles, HorngTzer YauFor random dregular graphs on N vertices with \(1 \ll d \ll N^{2/3}\), we develop a \(d^{1/2}\) expansion of the local eigenvalue distribution about the Kesten–McKay law up to order \(d^{3}\). This result is valid up to the edge of the spectrum. It implies that the eigenvalues of such random regular graphs are more rigid than those of Erdős–Rényi graphs of the same average degree. As a first application

Conformal actions of higher rank lattices on compact pseudoRiemannian manifolds Geom. Funct. Anal. (IF 2.148) Pub Date : 20200713
Vincent PecastaingWe investigate conformal actions of cocompact lattices in higherrank simple Lie groups on compact pseudoRiemannian manifolds. Our main result gives a general bound on the realrank of the lattice, which was already known for the action of the full Lie group by a result of Zimmer. When the realrank is maximal, we prove that the manifold is conformally flat. This indicates that a global conclusion

Symmetry results for critical anisotropic p Laplacian equations in convex cones Geom. Funct. Anal. (IF 2.148) Pub Date : 20200708
Giulio Ciraolo, Alessio Figalli, Alberto RoncoroniGiven \(n \ge 2\) and \(1

Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cusps Geom. Funct. Anal. (IF 2.148) Pub Date : 20200617
Werner Müller, Frédéric RochonOn an odddimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel–Serre compactification of the manifold. In a companion paper, this formula is used to derive exponential growth of torsion in cohomology of arithmetic groups.

Very functorial, very fast, and very easy resolution of singularities Geom. Funct. Anal. (IF 2.148) Pub Date : 20200613
Michael McQuillanThe main proposition, Theorem 1.2, is the existence for excellent Deligne–Mumford champ of characteristic zero of a resolution functor independent of the resolution process itself. Received wisdom was that this was impossible, but the counterexamples overlooked the possibility of using weighted blow ups. The fundamental local calculations take place in complete local rings, and are elementary in nature

Flows on the $$\mathbf{PGL(V)}$$PGL(V) Hitchin Component Geom. Funct. Anal. (IF 2.148) Pub Date : 20200514
Zhe Sun, Anna Wienhard, Tengren ZhangIn this article we define new flows on the Hitchin components for \(\mathrm {PGL}(V)\). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are associated to pair of pants in S and capture new phenomena which are not present in the case when \(n=2\). We determine a global coordinate system

Symplectic cohomology rings of affine varieties in the topological limit Geom. Funct. Anal. (IF 2.148) Pub Date : 20200429
Sheel Ganatra, Daniel PomerleanoWe construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety X, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification \((M,{\mathbf {D}})\) of X. We exhibit a broad class of pairs \((M,{\mathbf {D}})\) (characterized by the absence of relative holomorphic spheres or vanishing of certain

Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem Geom. Funct. Anal. (IF 2.148) Pub Date : 20200403
Ricardo A. E. Mendes, Marco RadeschiManifold submetries of the round sphere are a class of partitions of the round sphere that generalizes both singular Riemannian foliations, and the orbit decompositions by the orthogonal representations of compact groups. We exhibit a onetoone correspondence between such manifold submetries and maximal Laplacian algebras, thus solving the Inverse Invariant Theory problem for this class of partitions

Singular Vectors on Fractals and Projections of Selfsimilar Measures Geom. Funct. Anal. (IF 2.148) Pub Date : 20200402
Osama KhalilSingular vectors are those for which the quality of rational approximations provided by Dirichlet’s Theorem can be improved by arbitrarily small multiplicative constants. We provide an upper bound on the Hausdorff dimension of singular vectors lying on selfsimilar fractals in \({\mathbb {R}}^d\) satisfying the open set condition. The bound is in terms of quantities which are closely tied to Frostman

Anderson localization for multifrequency quasiperiodic operators on $$\pmb {\mathbb {Z}}^{d}$$Zd Geom. Funct. Anal. (IF 2.148) Pub Date : 20200401
Svetlana Jitomirskaya, Wencai Liu, Yunfeng ShiWe establish Anderson localization for general analytic kfrequency quasiperiodic operators on \({\mathbb {Z}}^d\) for arbitraryk, d.

Uryson Width and Volume Geom. Funct. Anal. (IF 2.148) Pub Date : 20200328
Panos PapasogluWe give a short proof of a theorem of Guth relating volume of balls and Uryson width. The same approach applies to Hausdorff content implying a recent result of Liokumovich–Lishak–Nabutovsky–Rotman. We show also that for any \(C>0\) there is a Riemannian metric g on a 3sphere such that \({\hbox {vol}}(S^3,g)=1\) and for any map \(f:S^3\rightarrow {\mathbb {R}}^2\) there is some \(x\in {\mathbb {R}}^2\)

Traceless AF embeddings and unsuspended $$\varvec{E}$$E theory Geom. Funct. Anal. (IF 2.148) Pub Date : 20200326
James GabeI show that quasidiagonality and AF embeddability are equivalent properties for traceless \(\mathrm C^*\)algebras and are characterised in terms of the primitive ideal space. For nuclear \(\mathrm C^*\)algebras the same characterisation determines when Connes and Higson’s Etheory can be unsuspended.

On the Random Wave Conjecture for Dihedral Maaß Forms Geom. Funct. Anal. (IF 2.148) Pub Date : 20200218
Peter Humphries, Rizwanur KhanWe prove two results on arithmetic quantum chaos for dihedral Maaß forms, both of which are manifestations of Berry’s random wave conjecture: Planck scale mass equidistribution and an asymptotic formula for the fourth moment. For level 1 forms, these results were previously known for Eisenstein series and conditionally on the generalised Lindelöf hypothesis for Hecke–Maaß eigenforms. A key aspect of

Contact Manifolds with Flexible Fillings Geom. Funct. Anal. (IF 2.148) Pub Date : 20200215
Oleg LazarevWe prove that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology. As an application, we show that in dimension at least 5 any almost contact class that has an almost Weinstein filling has infinitely many different contact structures. We also construct the first known infinite family of almost symplectomorphic Weinstein domains

Interplay Between Loewner and Dirichlet Energies via Conformal Welding and FlowLines Geom. Funct. Anal. (IF 2.148) Pub Date : 20200213
Fredrik Viklund, Yilin WangThe Loewner energy of a Jordan curve is the Dirichlet energy of its Loewner driving term. It is finite if and only if the curve is a Weil–Petersson quasicircle. In this paper, we describe cutting and welding operations on finite Dirichlet energy functions defined in the plane, allowing expression of the Loewner energy in terms of Dirichlet energy dissipation. We show that the Loewner energy of a unit

Optimal isoperimetric inequalities for surfaces in any codimension in CartanHadamard manifolds Geom. Funct. Anal. (IF 2.148) Pub Date : 20200213
Felix SchulzeLet \((M^n,g)\) be simply connected, complete, with nonpositive sectional curvatures, and \(\Sigma \) a 2dimensional closed integral current (or flat chain mod 2) with compact support in M. Let S be an area minimising integral 3current (resp. flat chain mod 2) such that \(\partial S = \Sigma \). We use a weak mean curvature flow, obtained via elliptic regularisation, starting from \(\Sigma \), to

Exponential mixing for a class of dissipative PDEs with bounded degenerate noise Geom. Funct. Anal. (IF 2.148) Pub Date : 20200213
Sergei Kuksin, Vahagn Nersesyan, Armen ShirikyanWe study a class of discretetime random dynamical systems with compact phase space. Assuming that the deterministic counterpart of the system in question possesses a dissipation property, its linearisation is approximately controllable, and the driving noise is bounded and has a decomposable structure, we prove that the corresponding family of Markov processes has a unique stationary measure, which