2019

最新文章

• SO(p,q)-Higgs bundles and Higher Teichmuller components AI翻译
  作者：Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; Garcia-Prada, Oscar; Gothen, Peter B.; Oliveira, Andre
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University System of Maryland; University of Maryland College Park; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidade do Porto; University of Tras-os-Montes & Alto Douro
  摘要：Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli sp...
• Enlargeability, foliations, and positive scalar curvature AI翻译
  作者：Benameur, Moulay-Tahar; Heitsch, James L.
  作者单位：Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
  摘要：We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold admits no PSC metric; that any metric of PSC on such a foliation is bounded by a multiple of the reciprocal of the foliation K-area of the ambient manifold; and that Connes' van...
• Equivalent descriptions of the loewner energy AI翻译
  作者：Wang, Yilin
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Loewner's equation provides a way to encode a simply connected domain or equivalently its uniformizing conformal map via a real-valued driving function of its boundary. The first main result of the present paper is that the Dirichlet energy of this driving function (also known as the Loewner energy) is equal to the Dirichlet energy of the log-derivative of the (appropriately defined) uniformizing conformal map. This description of the Loewner energy then enables to tie direct links with regula...
• The Balmer spectrum of the equivariant homotopy category of a finite abelian group AI翻译
  作者：Barthel, Tobias; Hausmann, Markus; Naumann, Niko; Nikolaus, Thomas; Noel, Justin; Stapleton, Nathaniel
  作者单位：University of Copenhagen; University of Regensburg; University of Munster; University of Kentucky
  摘要：For a finite abelian group A, we determine the Balmer spectrum of SpA, the compact objects in genuine A-spectra. This generalizes the case A=Z/pZ due to Balmer and Sanders (Invent Math 208(1):283-326, 2017), by establishing (a corrected version of) their logp-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn's blue-shift theorem for Tate-constructions (Kuhn in Invent Math 157(2):345-370, 2004).
• Sub-Riemannian interpolation inequalities AI翻译
  作者：Barilari, Davide; Rizzi, Luca
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
  摘要：We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients, whose properties are remarkably different with respect to the Riemannian case. As a byproduct, we characterize the cut locus as the set of points where the squared sub-Riemannian distance fails to be semiconvex, answering to a question raised by Figalli and Ri...
• Cantor spectrum of graphene in magnetic fields AI翻译
  作者：Becker, Simon; Han, Rui; Jitomirskaya, Svetlana
  作者单位：University of Cambridge; University System of Georgia; Georgia Institute of Technology; University of California System; University of California Irvine
  摘要：We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux phi/2 pi\documentclass through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.
• First order rigidity of non-uniform higher rank arithmetic groups AI翻译
  作者：Avni, Nir; Lubotzky, Alexander; Meiri, Chen
  作者单位：Northwestern University; Hebrew University of Jerusalem; Technion Israel Institute of Technology
  摘要：If is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example SLn(Z), n3) and is a finitely generated group that is elementarily equivalent to , then is isomorphic to Gamma.
• On the fine structure of the free boundary for the classical obstacle problem AI翻译
  作者：Figalli, Alessio; Serra, Joaquim
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：In the classical obstacle problem, the free boundary can be decomposed into regular and singular points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139:155-184, 1977; J Fourier Anal Appl 4:383-402, 1998), regular points consist of smooth hypersurfaces, while singular points are contained in a stratified union of C1 manifolds of varying dimension. In two dimensions, this C1 result has been improved to C1, by Weiss (Invent Math 138:23-50, 1999). In this paper we prove ...
• Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics AI翻译
  作者：Carrillo, J. A.; Hittmeir, S.; Volzone, B.; Yao, Y.
  作者单位：Imperial College London; University of Vienna; Parthenope University Naples; University System of Georgia; Georgia Institute of Technology
  摘要：We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrization techniques. Calculus of variations tools allow us to show the existence of glo...
• The derivation of the T3 energy-critical NLS from quantum many-body dynamics AI翻译
  作者：Chen, Xuwen; Holmer, Justin
  作者单位：University of Rochester; Brown University
  摘要：We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. Previously, the only result for the 3D energy critical case was Hong et al. (J Funct Anal 270(1):34-67, 2016), which proved the uniqueness part of the argument in the case of small solutions. I...