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作者：Cinkir, Zubeyir
作者单位：Zirve University
摘要：We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures were previously known to be true only for curves of good reduction, for curves of genus at most 4 and a few other special cases. We also either verify or improve the previous results. We relate the invariants involved in Zhang's Conjecture to the tau consta...
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作者：Cui, Guizhen; Tan, Lei
作者单位：Universite d'Angers; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We give a topological characterization of rational maps with disconnected Julia sets. Our results extend Thurston's characterization of post-critically finite rational maps. In place of iteration on Teichmuller space, we use quasiconformal surgery and Thurston's original result.
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作者：Iwaniec, Tadeusz; Koh, Ngin-Tee; Kovalev, Leonid V.; Onninen, Jani
作者单位：Syracuse University; University of Helsinki
摘要：The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms f : Omega ->(onto) Omega* between bounded doubly connected domains such that Omega <= Mod Omega* there exists, unique up to conformal authomorphisms of Omega, an energy-minimal diffeomorphism. Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results...
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作者：Vollaard, Inken; Wedhorn, Torsten
作者单位：University of Paderborn
摘要：We complete the study of the supersingular locus M-ss in the fiber at p of a Shimura variety attached to a unitary similitude group GU( 1, n - 1) over Q in the case that p is inert. This was started by the first author in Can. J. Math. 62, 668-720 ( 2010) where complete results were obtained for n = 2, 3. The supersingular locus M-ss is uniformized by a formal scheme N which is a moduli space of so-called unitary p-divisible groups. It depends on the choice of a unitary isocrystal N. We define...
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作者：Kudla, Stephen; Rapoport, Michael
作者单位：University of Bonn; University of Toronto
摘要：The supersingular locus in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1, n - 1) over Q is uniformized by a formal scheme N. In the case when p is an inert prime, we define special cycles Z(x) in N, associated to collections x of m 'special homomorphisms' with fundamental matrix T is an element of Herm(m)(O-k). When m = n and T is nonsingular, we show that the cycle Z(x) is either empty or is a union of components of the Ekedahl-Oort stratification, and we giv...
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作者：Dafermos, Mihalis; Rodnianski, Igor
作者单位：Princeton University; University of Cambridge
摘要：We consider Kerr spacetimes with parameters a and M such that vertical bar a vertical bar << M, Kerr-Newman spacetimes with parameters vertical bar Q vertical bar << M, vertical bar a vertical bar << M and more generally, stationary axisymmetric black hole exterior spacetimes (M, g) which are sufficiently close to a Schwarzschild metric with parameter M > 0 and whose Killing fields span the null generator of the event horizon. We show uniform boundedness on the exterior for solutions to the wa...
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作者：Bonk, Mario
作者单位：University of California System; University of California Los Angeles
摘要：Let S-i, i is an element of I, be a countable collection of Jordan curves in the extended complex plane (C) over cap that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map f : (C) over cap -> (C) over cap such that f (S-i) is a round circle for all i is an element of I. This implies that every Sierpinski carpet in (C) over cap whose peripheral circles are uniformly relative...
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作者：Varagnolo, M.; Vasserot, E.
作者单位：Universite Paris Cite; CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We prove a series of conjectures of Enomoto and Kashiwara on canonical bases and branching rules of affine Hecke algebras of type B. The main ingredient of the proof is a new graded Ext-algebra associated with quiver with involutions that we compute explicitly.
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作者：Klingler, B.
作者单位：Sorbonne Universite; Universite Paris Cite; Institute for Advanced Study - USA
摘要：We prove general local rigidity results for cocompact complex hyperbolic lattices using Hodge theory.
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作者：Roques, Julien
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：This paper deals with regular singular generalized q-hypergeometric equations with either large or small Galois groups. In particular, we consider the fundamental problem of finding appropriate Galoisian substitutes for the usual notion of local monodromy.
