2025

最新文章

• Bordifications of the moduli spaces of tropical curves and abelian varieties, and unstable cohomology of SLg(Z) AI翻译
  作者：Brown, Francis
  摘要：We con We construct bordifications of the moduli spaces of tropical curves and of tropical abelian varieties, and show that the tropical Torelli map extends to their bordifications. We prove that the classical bi-invariant differential forms studied by Cartan and others extend to these bordifications by studying their behaviour at infinity, and consequently deduce infinitely many new non-zero unstable classes in the cohomology of the general and special linear groups GL(g)(Z) and SLg(Z). In pa...
• Orbit equivalences of pseudo-Anosov flows AI翻译
  作者：Barthelme, Thomas; Frankel, Steven; Mann, Kathryn
  作者单位：Queens University - Canada; Washington University (WUSTL); Cornell University
  摘要：We prove a classification theorem for transitive Anosov and pseudo-Anosov flows on closed 3-manifolds, up to orbit equivalence. In many cases, flows on a 3-manifold M are completely determined by the set of free homotopy classes of their (unoriented) periodic orbits. The exceptional cases are flows with a special structure in their orbit space called a tree of scalloped regions; in these cases the set of free homotopy classes of unoriented periodic orbits together with the additional data of a...
• A random Hall-Paige conjecture AI翻译
  作者：Muyesser, Alp; Pokrovskiy, Alexey
  作者单位：University of Oxford; University of London; University College London
  摘要：A complete mapping of a group G is a bijection phi:G -> G such that x bar right arrow x phi(x) is also bijective. Hall and Paige conjectured in 1955 that a finite group G has a complete mapping whenever Pi(x is an element of G)x is the identity in the abelianization of G. This was confirmed in 2009 by Wilcox, Evans, and Bray with a proof using the classification of finite simple groups. In this paper, we give a combinatorial proof of a far-reaching generalisation of the Hall-Paige conjecture f...
• Curvature and sharp growth rates of log-quasimodes on compact manifolds AI翻译
  作者：Huang, Xiaoqi; Sogge, Christopher D.
  作者单位：Louisiana State University System; Louisiana State University; Johns Hopkins University
  摘要：We obtain new optimal estimates for the L-2(M)-> L-q(M), q is an element of(2,q(c)], q(c)=2(n+1)/(n-1), operator norms of spectral projection operators associated with spectral windows [lambda,lambda+delta(lambda)], with delta(lambda)=O((log lambda)(-1)) on compact Riemannian manifolds (M,g) of dimension n >= 2 all of whose sectional curvatures are nonpositive or negative. We show that these two different types of estimates are saturated on flat manifolds or manifolds all of whose sectional cu...
• Hausdorff dimension of the Apollonian gasket AI翻译
  作者：Vytnova, Polina L.; Wormell, Caroline L.
  作者单位：University of Surrey; University of Sydney
  摘要：The Apollonian gasket is a well-studied circle packing. Important properties of the packing, including the distribution of the circle radii, are governed by its Hausdorff dimension. No closed form is currently known for the Hausdorff dimension, and its computation is a special case of a more general and hard problem: effective, rigorous estimates of dimension of a parabolic limit set. In this paper we develop an efficient method for solving this problem which allows us to compute the dimension...
• Stability of the catenoid for the hyperbolic vanishing mean curvature equation outside symmetry AI翻译
  作者：Luhrmann, Jonas; Oh, Sung-Jin; Shahshahani, Sohrab
  作者单位：Texas A&M University System; Texas A&M University College Station; University of California System; University of California Berkeley; Korea Institute for Advanced Study (KIAS); University of Massachusetts System; University of Massachusetts Amherst
  摘要：We study the problem of stability of the catenoid, which is an asymptotically flat rotationally symmetric minimal surface in Euclidean space, viewed as a stationary solution to the hyperbolic vanishing mean curvature equation in Minkowski space. The latter is a quasilinear wave equation that constitutes the hyperbolic counterpart of the minimal surface equation in Euclidean space. Our main result is the nonlinear asymptotic stability, modulo suitable translation and boost (i.e., modulation), o...
• Logarithmic double ramification cycles AI翻译
  作者：Holmes, D.; Molcho, S.; Pandharipande, R.; Pixton, A.; Schmitt, J.
  作者单位：Leiden University; Leiden University - Excl LUMC; Sapienza University Rome; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Michigan System; University of Michigan
  摘要：Let A = (a1,..., an) be a vector of integers which sum to k(2g - 2+ n). The double ramification cycle DRg,A is an element of CHg(Mg,n) on the moduli space of curves is the virtual class of an Abel-Jacobi locus of pointed curves (C, x1,..., xn) satisfying OC(Sigma i=1naixi)similar or equal to(omega Clog)k.. The Abel-Jacobi construction requires log blow-ups of M g,n to resolve the indeterminacies of the Abel-Jacobi map. Holmes (J. Inst. Math. Jussieu 2019) has shown that DRg, A admits a canonic...
• Étale cohomology of algebraic varieties over Stein compacta AI翻译
  作者：Benoist, Olivier
  作者单位：Centre National de la Recherche Scientifique (CNRS)
  摘要：We prove a comparison theorem between the & eacute;tale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Stein compact subset of a normal complex space of dimension n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...
• A generalized Legendre duality relation and Gaussian saturation AI翻译
  作者：Nakamura, Shohei; Tsuji, Hiroshi
  作者单位：University of Osaka; University of Birmingham; Saitama University
  摘要：Motivated by the barycenter problem in optimal transportation theory, Kolesnikov-Werner recently extended the concept of the Legendre duality relation from two functions to multiple functions. We further generalize this duality relation and then establish the centered Gaussian saturation property for a Blaschke-Santal & oacute;-type inequality associated with it. Our approach to understanding this generalized Legendre duality relation is based on the observation that directly links Legendre du...
• Renormalization group and elliptic homogenization in high contrast AI翻译
  作者：Armstrong, Scott; Kuusi, Tuomo
  作者单位：New York University; University of Helsinki
  摘要：We prove a quantitative estimate for the homogenization length scale in terms of the ellipticity ratio Lambda/lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Lambda /\lambda $\end{document} of the coefficient field. This upper bound applies to high-contrast elliptic equations exhibiting near-critical behavior...