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Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-03-04 Sahana Vasudevan
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Coalescence of Geodesics and the BKS Midpoint Problem in Planar First-Passage Percolation Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-21 Barbara Dembin, Dor Elboim, Ron Peled
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Augmentations, Fillings, and Clusters Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-21 Honghao Gao, Linhui Shen, Daping Weng
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On Closed Geodesics in Lorentz Manifolds Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-15 S. Allout, A. Belkacem, A. Zeghib
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A New Complete Two-Dimensional Shrinking Gradient Kähler-Ricci Soliton Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-14 Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon, Alix Deruelle
We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of \(\mathbb{C}\times \mathbb{P}^{1}\) at one point. This completes the classification of such solitons in two complex dimensions.
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Non-isomorphism of A∗n,2≤n≤∞, for a non-separable abelian von Neumann algebra A Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-14 Rémi Boutonnet, Daniel Drimbe, Adrian Ioana, Sorin Popa
We prove that if A is a non-separable abelian tracial von Neuman algebra then its free powers A∗n,2≤n≤∞, are mutually non-isomorphic and with trivial fundamental group, \(\mathcal{F}(A^{*n})=1\), whenever 2≤n<∞. This settles the non-separable version of the free group factor problem.
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Weakly Bounded Cohomology Classes and a Counterexample to a Conjecture of Gromov Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-14
Abstract We exhibit a group of type F whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds.
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Homology Growth, Hyperbolization, and Fibering Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-14 Grigori Avramidi, Boris Okun, Kevin Schreve
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Quasiregular Values and Rickman’s Picard Theorem Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-14 Ilmari Kangasniemi, Jani Onninen
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Partial Hyperbolicity and Pseudo-Anosov Dynamics Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-07 Sergio R. Fenley, Rafael Potrie
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A Metric Fixed Point Theorem and Some of Its Applications Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-07 Anders Karlsson
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new for isometries of convex sets of Banach spaces as well as for non-locally compact CAT(0)-spaces and injective spaces. Examples of actions on non-proper CAT(0)-spaces come from the study of diffeomorphism groups, birational transformations, and
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On the Almost Reducibility Conjecture Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-05
Abstract Avila’s Almost Reducibility Conjecture (ARC) is a powerful statement linking purely analytic and dynamical properties of analytic one-frequency \(SL(2,{\mathbb{R}})\) cocycles. It is also a fundamental tool in the study of spectral theory of analytic one-frequency Schrödinger operators, with many striking consequences, allowing to give a detailed characterization of the subcritical region
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On the Dimension of Exceptional Parameters for Nonlinear Projections, and the Discretized Elekes-Rónyai Theorem Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-05 Orit E. Raz, Joshua Zahl
We consider four related problems. (1) Obtaining dimension estimates for the set of exceptional vantage points for the pinned Falconer distance problem. (2) Nonlinear projection theorems, in the spirit of Kaufman, Bourgain, and Shmerkin. (3) The parallelizability of planar d-webs. (4) The Elekes-Rónyai theorem on expanding polynomials. Given a Borel set A in the plane, we study the set of exceptional
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Kaufman and Falconer Estimates for Radial Projections and a Continuum Version of Beck’s Theorem Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-05 Tuomas Orponen, Pablo Shmerkin, Hong Wang
We provide several new answers on the question: how do radial projections distort the dimension of planar sets? Let \(X,Y \subset \mathbb{R}^{2}\) be non-empty Borel sets. If X is not contained in any line, we prove that $$ \sup _{x \in X} \dim _{\mathrm {H}}\pi _{x}(Y \, \setminus \, \{x\}) \geq \min \{ \dim _{\mathrm {H}}X,\dim _{\mathrm {H}}Y,1\}. $$ If dimHY>1, we have the following improved lower
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CAT(0) Spaces of Higher Rank I Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-02
Abstract A CAT(0) space has rank at least n if every geodesic lies in an n-flat. Ballmann’s Higher Rank Rigidity Conjecture predicts that a CAT(0) space of rank at least 2 with a geometric group action is rigid – isometric to a Riemannian symmetric space, a Euclidean building, or splits as a metric product. This paper is the first in a series motivated by Ballmann’s conjecture. Here we prove that a
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Gromov’s Tori Are Optimal Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-01
Abstract We give an optimal bound on normal curvatures of immersed n-torus in a Euclidean ball of large dimension.
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Mean Convex Smoothing of Mean Convex Cones Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-01 Zhihan Wang
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex self-expander asymptotic to it near infinity. These two together confirm a conjecture of Lawson (Geom. Meas. Theor. Calcu. Var. 44:441, 1986, Problem 5.7).
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Two Rigidity Results for Stable Minimal Hypersurfaces Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-01 Giovanni Catino, Paolo Mastrolia, Alberto Roncoroni
The aim of this paper is to prove two results concerning the rigidity of complete, immersed, orientable, stable minimal hypersurfaces: we show that they are hyperplane in R4, while they do not exist in positively curved closed Riemannian (n+1)-manifold when n≤5; in particular, there are no stable minimal hypersurfaces in Sn+1 when n≤5. The first result was recently proved also by Chodosh and Li, and
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Extremal Affine Subspaces and Khintchine-Jarník Type Theorems Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-02-01
Abstract We prove a conjecture of Kleinbock which gives a clear-cut classification of all extremal affine subspaces of \(\mathbb{R}^{n}\) . We also give an essentially complete classification of all Khintchine type affine subspaces, except for some boundary cases within two logarithmic scales. More general Jarník type theorems are proved as well, sometimes without the monotonicity of the approximation
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Odd Distances in Colourings of the Plane Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-01-30 James Davies
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.
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A New Regularized Siegel-Weil Type Formula. Part I Geom. Funct. Anal. (IF 2.2) Pub Date : 2024-01-22 David Ginzburg, David Soudry
In this paper, we prove a formula, realizing certain residual Eisenstein series on symplectic groups as regularized kernel integrals. These Eisenstein series, as well as the kernel integrals, are attached to Speh representations. This forms an initial step to a new type of a regularized Siegel-Weil formula that we propose. This new formula bears the same relation to the generalized doubling integrals
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Relations between scaling exponents in unimodular random graphs Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-11-09 James R. Lee
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GOE statistics on the moduli space of surfaces of large genus Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-11-02 Zeév Rudnick
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Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-10-31 Jeffrey Galkowski, Leonid Parnovski, Roman Shterenberg
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Bers’ simultaneous uniformization and the intersection of Poincaré holonomy varieties Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-10-31 Shinpei Baba
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Concentration of invariant means and dynamics of chain stabilizers in continuous geometries Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-10-12 Friedrich Martin Schneider
We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma’s martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann’s continuous geometries
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Contribution of n-cylinder square-tiled surfaces to Masur–Veech volume of $\mathcal{H}(2g-2)$ Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-10-12 Ivan Yakovlev
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A nonabelian Brunn–Minkowski inequality Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-07-05 Yifan Jing, Chieu-Minh Tran, Ruixiang Zhang
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Tori Approximation of Families of Diagonally Invariant Measures Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-07-04 Omri Nisan Solan, Yuval Yifrach
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Approximate Lattices in Higher-Rank Semi-Simple Groups Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-30 Simon Machado
We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.
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Local Connectivity of the Mandelbrot Set at Some Satellite Parameters of Bounded Type Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-26 Dzmitry Dudko, Mikhail Lyubich
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On the Alesker-Verbitsky Conjecture on HyperKähler Manifolds Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-20 Sławomir Dinew, Marcin Sroka
We solve the quaternionic Monge–Ampère equation on hyperKähler manifolds. In this way we prove the ansatz for the conjecture raised by Alesker and Verbitsky claiming that this equation should be solvable on any hyperKähler with torsion manifold, at least when the canonical bundle is trivial holomorphically. The novelty in our approach is that we do not assume any flatness of the underlying hypercomplex
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Threshold for Steiner triple systems Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-19 Ashwin Sah, Mehtaab Sawhney, Michael Simkin
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The Branched Deformations of the Special Lagrangian Submanifolds Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-19 Siqi He
In this paper, we investigate the branched deformations of immersed compact special Lagrangian submanifolds. If there exists a nondegenerate \(\mathbb {Z}_2\) harmonic 1-form over a special Lagrangian submanifold L, we construct a family of immersed special Lagrangian submanifolds \(\tilde{L}_t\), that are diffeomorphic to a branched covering of L and \(\tilde{L}_t\) converge to 2L as current. This
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An exotic II $$_1$$ factor without property Gamma Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-17 Ionuţ Chifan, Adrian Ioana, Srivatsav Kunnawalkam Elayavalli
We introduce a new iterative amalgamated free product construction of II\(_1\) factors, and use it to construct a separable II\(_1\) factor which does not have property Gamma and is not elementarily equivalent to the free group factor \(\text {L}(\mathbb F_n)\), for any \(2\le n\le \infty \). This provides the first explicit example of two non-elementarily equivalent II\(_1\) factors without property
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Additive problems with almost prime squares Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-19 Valentin Blomer, Lasse Grimmelt, Junxian Li, Simon L. Rydin Myerson
We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We likewise treat representations of shifted primes \(p-1\) as sums of two almost prime squares. The methods involve a combination of analytic, automorphic and algebraic
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Commuting symplectomorphisms on a surface and the flux homomorphism Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-06-14 Morimichi Kawasaki, Mitsuaki Kimura, Takahiro Matsushita, Masato Mimura
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Automorphisms of groups and a higher rank JSJ decomposition I: RAAGs and a higher rank Makanin-Razborov diagram Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-05-16 Z. Sela
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. In this sequence of papers we study the automorphisms of a hierarchically hyperbolic group that satisfies some weak acylindricity conditions. To study these automorphisms we construct an object that can
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Mapping class group orbit closures for non-orientable surfaces Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-05-12 Viveka Erlandsson, Matthieu Gendulphe, Irene Pasquinelli, Juan Souto
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Arboreal structures on groups and the associated boundaries Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-05-03 Anna Erschler, Vadim A. Kaimanovich
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Gaussian Gabor frames, Seshadri constants and generalized Buser–Sarnak invariants Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-04-24 Franz Luef, Xu Wang
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kähler geometry such as Hörmander’s \({\overline{\partial }}\)-\(L^2\) estimate with singular weight, Demailly’s Calabi–Yau method for Kähler currents and a Kähler-variant generalization of the symplectic embedding theorem of McDuff–Polterovich for ellipsoids. Our approach is based on the well-known link between
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The metric measure boundary of spaces with Ricci curvature bounded below Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-04-20 Elia Bruè, Andrea Mondino, Daniele Semola
We solve a conjecture raised by Kapovitch, Lytchak and Petrunin in [KLP21] by showing that the metric measure boundary is vanishing on any \({{\,\textrm{RCD}\,}}(K,N)\) space \((X,{\textsf{d}},{\mathscr {H}}^N)\) without boundary. Our result, combined with [KLP21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin
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On the random Chowla conjecture Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-04-18 Oleksiy Klurman, Ilya D. Shkredov, Max Wenqiang Xu
We show that for a Steinhaus random multiplicative function \(f:{\mathbb {N}}\rightarrow {\mathbb {D}}\) and any polynomial \(P(x)\in {\mathbb {Z}}[x]\) of \(\deg P\ge 2\) which is not of the form \(w(x+c)^{d}\) for some \(w\in {\mathbb {Z}}\), \(c\in {\mathbb {Q}}\), we have $$\begin{aligned} \frac{1}{\sqrt{N}}\sum _{n\le N} f(P(n)) \xrightarrow {d} {{\mathcal {C}}}{{\mathcal {N}}}(0,1), \end{aligned}$$
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Measure bound for translation surfaces with short saddle connections Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-04-11 Benjamin Dozier
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Measure rigidity of Anosov flows via the factorization method Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-03-19 Asaf Katz
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Uniqueness of some cylindrical tangent cones to special Lagrangians Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-03-13 Tristan C. Collins, Yang Li
We show that if an exact special Lagrangian \(N\subset {\mathbb {C}}^n\) has a multiplicity one, cylindrical tangent cone of the form \({\mathbb {R}}^{k}\times {\textbf{C}}\) where \({\textbf{C}}\) is a special Lagrangian cone with smooth, connected link, then this tangent cone is unique provided \({\textbf{C}}\) satisfies an integrability condition. This applies, for example, when \({\textbf{C}}=
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The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-03-10 Artur Avila, David Damanik, Anton Gorodetski
We consider Schrödinger operators in \(\ell ^2({\mathbb Z})\) whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact metric space and a continuous sampling function, we show that the almost sure spectrum arises in an explicitly described way from the unperturbed spectrum
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From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-02-09 Jan Kotrbatý, Thomas Wannerer
The Alesker–Bernig–Schuster theorem asserts that each irreducible representation of the special orthogonal group appears with multiplicity at most one as a subrepresentation of the space of continuous translation-invariant valuations with fixed degree of homogeneity. Moreover, the theorem describes in terms of highest weights which irreducible representations appear with multiplicity one. In this paper
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A transfer principle: from periods to isoperiodic foliations Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-02-03 Gabriel Calsamiglia, Bertrand Deroin, Stefano Francaviglia
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On the local systolic optimality of Zoll contact forms Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-02-03 Alberto Abbondandolo, Gabriele Benedetti
We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this result are: (1) sharp local systolic inequalities for Riemannian and Finsler metrics close to Zoll ones, (2) the perturbative case of a conjecture of Viterbo on the symplectic capacity of convex bodies, (3) a generalization
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Exact dimension of Furstenberg measures Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-02-01 François Ledrappier, Pablo Lessa
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Isometric group actions with vanishing rate of escape on $$\textrm{CAT}(0)$$ spaces Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-01-24 Hiroyasu Izeki
Let \(Y=(Y,d)\) be a \(\textrm{CAT}(0)\) space which is either proper or of finite telescopic dimension, and \(\Gamma \) a countable group equipped with a symmetric and nondegenerate probability measure \(\mu \). Suppose that \(\Gamma \) acts on Y via a homomorphism \(\rho :\Gamma \rightarrow \textrm{Isom}({Y})\), where \(\textrm{Isom}({Y})\) denotes the isometry group of Y, and that the action given
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Quantitative weak mixing for interval exchange transformations Geom. Funct. Anal. (IF 2.2) Pub Date : 2023-01-18 Artur Avila, Giovanni Forni, Pedram Safaee
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Large deviations for the interchange process on the interval and incompressible flows Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-11-15 Michał Kotowski, Bálint Virág
We use the framework of permuton processes to show that large deviations of the interchange process are controlled by the Dirichlet energy. This establishes a rigorous connection between processes of permutations and one-dimensional incompressible Euler equations. While our large deviation upper bound is valid in general, the lower bound applies to processes corresponding to incompressible flows, studied
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Symplectic cohomology and a conjecture of Viterbo Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-10-31 Egor Shelukhin
We identify a new class of closed smooth manifolds for which there exists a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit cotangent disk bundle. This settles a well-known conjecture of Viterbo from 2007 as the special case of \(T^n,\) which has been completely open for \(n>1\). Our methods are different and more intrinsic than those of the previous
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On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-10-25 Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
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Diameter estimates for long-time solutions of the Kähler–Ricci flow Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-10-22 Wangjian Jian, Jian Song
It is well known that the Kähler–Ricci flow on a Kähler manifold X admits a long-time solution if and only if X is a minimal model, i.e., the canonical line bundle \(K_X\) is nef. The abundance conjecture in algebraic geometry predicts that \(K_X\) must be semi-ample when X is a projective minimal model. We prove that if \(K_X\) is semi-ample, then the diameter is uniformly bounded for long-time solutions
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Existence of Birkhoff sections for Kupka–Smale Reeb flows of closed contact 3-manifolds Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-10-06 Gonzalo Contreras, Marco Mazzucchelli
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The generalized doubling method: local theory Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-09-29 Yuanqing Cai, Solomon Friedberg, Eyal Kaplan
A fundamental difficulty in the study of automorphic representations, representations of p-adic groups and the Langlands program is to handle the non-generic case. In a recent collaboration with David Ginzburg, we presented a new integral representation for the tensor product L-functions of \(G\times {{\,\mathrm{GL}\,}}_k\) where G is a classical group, that applies to all cuspidal automorphic representations
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Poincaré profiles of Lie groups and a coarse geometric dichotomy Geom. Funct. Anal. (IF 2.2) Pub Date : 2022-09-27 David Hume, John M. Mackay, Romain Tessera