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作者：de Fernex, Tommaso
作者单位：Utah System of Higher Education; University of Utah
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作者：Filip, Simion
作者单位：University of Chicago
摘要：We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant subbundles must vary polynomially on affine manifolds. All results apply to tensor powers of the cocycle and this implies that the measurable and real-analytic algebraic hulls coincide. We also prove that affine manifolds typically parametrize Jacobians with non-trivial endomorphisms. If the...
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作者：Oh, Sung-Jin; Tataru, Daniel
作者单位：University of California System; University of California Berkeley
摘要：This article constitutes the final and main part of a three-paper sequence (Ann PDE, 2016. doi:10.1007/s40818-016-0006-4; Oh and Tataru, 2015. arXiv:1503.01561), whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on R1+4 for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers (Ann PDE, 2016. doi:10.1007/s40818-016-0006-4; Oh and Tataru, 2...
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作者：Contreras, Gonzalo
作者单位：CIMAT - Centro de Investigacion en Matematicas
摘要：We prove that for an expanding transformation the maximizing measures of a generic Lipschitz function are supported on a single periodic orbit.
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作者：De Simoi, Jacopo; Liverani, Carlangelo
作者单位：University of Toronto; University of Rome Tor Vergata
摘要：We consider a class of partially hyperbolic systems on described by maps where are expanding maps of the circle. For sufficiently small and generic in an open set, we precisely classify the SRB measures for and their statistical properties, including exponential decay of correlation for Holder observables with explicit and nearly optimal bounds on the decay rate.
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作者：Uhlmann, Gunther; Vasy, Andras
作者单位：University of Washington; University of Washington Seattle; University of Helsinki; Hong Kong University of Science & Technology; Stanford University
摘要：Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic X-ray transform is globally injective. In addition we prove stability estimates and propose a layer stripping type algorithm for reconstruction.
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作者：Wu, Damin; Yau, Shing-Tung
作者单位：University of Connecticut; Harvard University
摘要：In this note we show that if a projective manifold admits a Kahler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample. This confirms a conjecture of the second author.
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作者：Aizenbud, Avraham; Avni, Nir
作者单位：Weizmann Institute of Science; Northwestern University
摘要：Let G be a semisimple algebraic group defined over , and let be a compact open subgroup of . We relate the asymptotic representation theory of and the singularities of the moduli space of G-local systems on a smooth projective curve, proving new theorems about both:We prove that there is a constant C, independent of G, such that the number of n-dimensional representations of grows slower than , confirming a conjecture of Larsen and Lubotzky. In fact, we can take . We also prove the same bounds...
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作者：Kim, Inkang; Lecuire, Cyril; Ohshika, Ken'ichi
作者单位：Korea Institute for Advanced Study (KIAS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Osaka
摘要：We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination. We prove that if this limit projective lamination is doubly incompressible, then the sequence has compact closure in the deformation space. As a consequence we generalise Thurston's double limit theorem and solve his conjecture on convergence of fun...
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作者：McMullen, Curtis T.
作者单位：Harvard University
