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• Existence and uniqueness of the Liouville quantum gravity metric for γ ∈(0,2) AI翻译
  作者：Gwynne, Ewain; Miller, Jason
  作者单位：University of Cambridge
  摘要：We show that for each gamma is an element of (0, 2), there is a unique metric (i.e., distance function) associated with gamma-Liouville quantum gravity (LQG). More precisely, we show that for the whole-plane Gaussian free field (GFF) h, there is a unique random metric D-h associated with the Riemannian metric tensor e(gamma h)(dx(2) + dy(2)) on C which is characterized by a certain list of axioms: it is locally determined by h and it transforms appropriately when either adding a continuous fun...
• On a conjecture of Furusho over function fields AI翻译
  作者：Chang, Chieh-Yu; Mishiba, Yoshinori
  作者单位：National Tsing Hua University; University of the Ryukyus
  摘要：In the classical theory of multiple zeta values (MZV's), Furusho pro-posed a conjecture asserting that the p-adic MZV's satisfy the same Q-linear relations that their corresponding real-valued MZV counterparts satisfy. In this paper, we verify a stronger version of a function field analogue of Furusho's conjecture in the sense that we are able to deal with all linear relations over an algebraic closure of the given rational function field, not just the rational linear relations. To each tuple ...
• Local limits of uniform triangulations in high genus AI翻译
  作者：Budzinski, Thomas; Louf, Baptiste
  作者单位：University of British Columbia; Universite Paris Cite
  摘要：We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the planar stochastic hyperbolic triangulations (PSHT) defined in Curien (Probab Theory Relat Fields 165(3):509-540, 2016). The proof relies on a combinatorial argument and the Goulden-Jackson recurrence relation to obtain tightness, and probabilistic arguments showing the uniqueness of the limit. As a consequence, we obtain asympto...
• Constant mean curvature spheres in homogeneous three-manifolds AI翻译
  作者：Meeks, William H., III; Mira, Pablo; Perez, Joaquin; Ros, Antonio
  作者单位：University of Massachusetts System; University of Massachusetts Amherst; Universidad Politecnica de Cartagena; University of Granada; University of Granada
  摘要：We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.
• Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems AI翻译
  作者：Kang, Moon-Jin; Vasseur, Alexis F.
  作者单位：Korea Advanced Institute of Science & Technology (KAIST); University of Texas System; University of Texas Austin
  摘要：We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the vanishing viscosity limit, we show a contraction property for any large perturbations of viscous shocks to the Navier-Stokes system. The contraction estimate does not depend on the strength of the viscosity. This provides a good control on the inviscid limit process. We prove that, for any initial...
• New curvature conditions for the Bochner Technique AI翻译
  作者：Petersen, Peter; Wink, Matthias
  作者单位：University of California System; University of California Los Angeles
  摘要：We show that manifolds with [n/2]-positive curvature operators are rational homology spheres. This follows from a more general vanishing and estimation theorem for the pth Betti number of closed n-dimensional Riemannian manifolds with a lower bound on the average of the lowest n - p eigenvalues of the curvature operator. This generalizes results due to D. Meyer, Gallot-Meyer, and Gallot.
• Rigidity of Riemannian embeddings of discrete metric spaces AI翻译
  作者：Eilat, Matan; Klartag, Bo'az
  作者单位：Weizmann Institute of Science
  摘要：Let M be a complete, connected Riemannian surface and suppose that S subset of M is a discrete subset. What can we learn about M from the knowledge of all Riemannian distances between pairs of points of S? We prove that if the distances in S correspond to the distances in a 2-dimensional lattice, or more generally in an arbitrary net in R-2, then M is isometric to the Euclidean plane. We thus find that Riemannian embeddings of certain discrete metric spaces are rather rigid. A corollary is tha...
• Homological branching law for (GLn+1(F), GLn(F)): projectivity and indecomposability AI翻译
  作者：Chan, Kei Yuen
  作者单位：Fudan University
  摘要：Let F be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from GL(n+1)( F) to GL(n)( F). A main result shows that each Bernstein component of an irreducible smooth representation of GL(n+1)( F) restricted to GL(n)(F) is indecomposable. We also classify all irreducible representations which are projective when restricting from GL(n+1)( F) to GL(n)( F). A main tool of our study is a notion of left and right derivatives, ext...
• Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones AI翻译
  作者：Chen, Xuemiao; Sun, Song
  作者单位：University System of Maryland; University of Maryland College Park; University of California System; University of California Berkeley
  摘要：In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.
• Nuclear dimension of simple C*-algebras AI翻译
  作者：Castillejos, Jorge; Evington, Samuel; Tikuisis, Aaron; White, Stuart; Winter, Wilhelm
  作者单位：KU Leuven; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Oxford; University of Ottawa; University of Glasgow; University of Munster
  摘要：We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.