Inventiones mathematicae

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• The Smale conjecture and min-max theory AI翻译
  作者：Ketover, Daniel; Liokumovich, Yevgeny
  作者单位：Rutgers University System; Rutgers University New Brunswick; University of Toronto; University Toronto Mississauga
  摘要：We give a new proof of the Smale conjecture for RP3 and all lens spaces using minimal surfaces and min-max theory. For RP3, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.
• Solvability of the Lp Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph AI翻译
  作者：Bortz, Simon; Hofmann, Steve; Martell, Jose Maria; Nystrom, Kaj
  作者单位：University of Alabama System; University of Alabama Tuscaloosa; University of Missouri System; University of Missouri Columbia; Universidad Carlos III de Madrid; Complutense University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); Autonomous University of Madrid; Uppsala University
  摘要：We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is a parabolic A(infinity) weight with respect to surface measure (which in turn is equivalent to L(p )solvability of the Dirichlet problem for some finite p), then the function defining the graph has a half-order time derivative in the space of (parabolic) bounded mean oscillation. Equivalently, we prove that the A(infinity) property of caloric measure implies, in this case, that t...
• Exponential scalar mixing for the 2D Navier-Stokes equations with degenerate stochastic forcing AI翻译
  作者：Cooperman, William; Rowan, Keefer
  作者单位：New York University
  摘要：We show exponential mixing of passive scalars advected by a solution to the stochastic Navier-Stokes equations with finitely many (e.g. four) forced modes satisfying a hypoellipticity condition. Our proof combines the asymptotic strong Feller framework of Hairer and Mattingly with the mixing theory of Bedrossian, Blumenthal, and Punshon-Smith.
• Strict comparison in reduced group C*-algebras AI翻译
  作者：Amrutam, Tattwamasi; Gao, David; Elayavalli, Srivatsav Kunnawalkam; Patchell, Gregory
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of California System; University of California San Diego
  摘要：We prove that for every n is an element of N such that n >= 2, the reduced group C*-algebras of the countable free groups Cr*(Fn) have strict comparison. Our method works in a general setting: for every finitely generated acylindrically hyperbolic group G with trivial finite radical and the rapid decay property, we have Cr*(G) have strict comparison. This work also has several applications in the theory of C*-algebras including: resolving Leonel Robert's selflessness problem for Cr*(G) uniquen...
• The geometry of permutation modules AI翻译
  作者：Balmer, Paul; Gallauer, Martin
  作者单位：University of California System; University of California Los Angeles
  摘要：We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the problem to elementary abelian groups and then by using a twisted form of cohomology to express the spectrum locally in terms of the graded endomorphism ring of the unit. Together, these results yield a classification of thick and of localizing ideals.
• Voronoi conjecture for five-dimensional parallelohedra AI翻译
  作者：Garber, Alexey
  作者单位：University of Texas System; University of Texas Rio Grande Valley
  摘要：We prove the Voronoi conjecture for five-dimensional parallelohedra. Namely, we show that if a convex five-dimensional polytope P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$P$\end{document} tiles R5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} ...
• Intermediate complex structure limit for Calabi-Yau metrics AI翻译
  作者：Li, Yang
  摘要：We study polarised degenerations of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n$\end{document}-dimensional Calabi-Yau hypersurfaces {F0F1 & mldr;Fm+tF=0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} ...
• Sharp bounds on the Nusselt number in Rayleigh-Bénard convection and a bilinear estimate by Coifman-Meyer AI翻译
  作者：Chanillo, Sagun; Malchiodi, Andrea
  作者单位：Rutgers University System; Rutgers University New Brunswick; Scuola Normale Superiore di Pisa
  摘要：We prove a conjecture in fluid dynamics concerning optimal bounds for heat transportation in the infinite Prandtl number limit and for large Rayleigh number Ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Ra}$\end{document}, predicted in (Howard in Proceedings of the 11th International Congress of Applied ...
• Quillen stratification in equivariant homotopy theory AI翻译
  作者：Barthel, Tobias; Castellana, Natalia; Heard, Drew; Naumann, Niko; Pol, Luca
  作者单位：Max Planck Society; Autonomous University of Barcelona; Centre de Recerca Matematica (CRM); Norwegian University of Science & Technology (NTNU); University of Regensburg
  摘要：We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document}, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as coefficients, and s...
• On the monotonicity of the Fisher information for the Boltzmann equation AI翻译
  作者：Imbert, Cyril; Silvestre, Luis; Villani, Cedric
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); University of Chicago; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：We prove that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all classical interactions derived from systems of particles. For general collision kernels, a sufficient condition for the monotonicity of the Fisher information along the flow is related to the best constant for an integro-differential inequality for functions on the sphere, which belongs in the family of the Log-Sobol...