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作者：Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie
作者单位：Princeton University; Universite PSL; Ecole Normale Superieure (ENS)
摘要：This is the main paper in a sequence in which we give a complete proof of the bounded curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the -norm of the curvature and a lower bound on the volume radius of the corresponding initial data set. We note that though the result is not optimal with respect to the scaling of the Einstein equations, it is nevertheless critical with respect to its causal geomet...
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作者：Contreras, G.; Figalli, A.; Rifford, L.
作者单位：University of Texas System; University of Texas Austin; Universite Cote d'Azur
摘要：Given a Tonelli Hamiltonian of class on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the topology for which the Aubry set is hyperbolic in its energy level.
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作者：Emerton, Matthew; Gee, Toby; Savitt, David
作者单位：University of Chicago; Imperial College London; University of Arizona
摘要：We prove the main conjectures of Breuil (J Reine Angew Math, 2012) (including a generalisation from the principal series to the cuspidal case) and Demb,l, (J Reine Angew Math, 2012), subject to a mild global hypothesis that we make in order to apply certain theorems. More precisely, we prove a multiplicity one result for the mod cohomology of a Shimura curve at Iwahori level, and we show that certain apparently globally defined lattices in the cohomology of Shimura curves are determined by the...
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作者：Bourgain, Jean; Li, Dong
作者单位：Institute for Advanced Study - USA; University of British Columbia
摘要：For the -dimensional incompressible Euler equation, the standard energy method gives local wellposedness for initial velocity in Sobolev space , . The borderline case was a folklore open problem. In this paper we consider the physical dimension and show that if we perturb any given smooth initial data in norm, then the corresponding solution can have infinite norm instantaneously at . In a companion paper [1] we settle the 3D and more general cases. The constructed solutions are unique and eve...
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作者：Berndtsson, Bo
作者单位：Chalmers University of Technology
摘要：For a metric on the anticanonical bundle, , of a Fano manifold we consider the volume of In earlier papers we have proved that the logarithm of the volume is concave along geodesics in the space of positively curved metrics on . Our main result here is that the concavity is strict unless the geodesic comes from the flow of a holomorphic vector field on , even with very low regularity assumptions on the geodesic. As a consequence we get a simplified proof of the Bando-Mabuchi uniqueness theorem...
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作者：Brendle, Simon
作者单位：Stanford University
摘要：We consider a family of embedded, mean convex hypersurfaces which evolve by the mean curvature flow. It follows from general results of White that the inscribed radius at each point on the hypersurface is at least , where is a positive constant that depends only on the initial data. Andrews recently gave a new proof of that fact using the maximum principle. In this paper, we show that the inscribed radius is at least at each point where the curvature is sufficiently large.
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作者：Brendle, Tara; Margalit, Dan; Putman, Andrew
作者单位：University System of Georgia; Georgia Institute of Technology; University of Glasgow; Rice University
摘要：We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t = -1 and also the fundamental group of the branch locus of the period mapping, and so we obtain analogous generating sets for those. One application is that each component in Torelli space of the locus o...
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作者：Avila, Artur; Krikorian, Raphael
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We develop a local theory of multidimensional quasiperiodic cocycles which are not homotopic to a constant. It describes a -open neighborhood of cocycles of rotations and applies irrespective of arithmetic conditions on the frequency, being much more robust than the local theory of cocycles homotopic to a constant. Our analysis is centered around the notion of monotonicity with respect to some dynamical variable. For such monotonic cocycles, we obtain a sharp rigidity result, minimality of the...
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作者：Kaletha, Tasho
作者单位：Princeton University
摘要：We provide an explicit construction of the local Langlands correspondence for general tamely-ramified reductive p-adic groups and a class of wildly ramified Langlands parameters. Furthermore, we verify that our construction satisfies many expected properties of such a correspondence. More precisely, we show that each -packet we construct admits a parameterization in terms of the Langlands dual group, contains a unique generic element for a fixed Whittaker datum, satisfies the formal degree con...
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作者：Matheus, Carlos; Moeller, Martin; Yoccoz, Jean-Christophe
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Goethe University Frankfurt; Universite PSL; College de France
摘要：We present a Galois-theoretical criterion for the simplicity of the Lyapunov spectrum of the Kontsevich-Zorich cocycle over the Teichmuller flow on the -orbit of a square-tiled surface. The simplicity of the Lyapunov spectrum has been proved by A. Avila and M. Viana with respect to the so-called Masur-Veech measures associated to connected components of moduli spaces of translation surfaces, but is not always true for square-tiled surfaces of genus . We apply our criterion to square-tiled surf...
