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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：Preiss, David; Speight, Gareth
作者单位：University of Warwick; Scuola Normale Superiore di Pisa
摘要：We show that if then there exists a Lebesgue null set in containing a point of differentiability of each Lipschitz function ; in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of -porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.
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作者：Bridson, Martin R.; Wilton, Henry
作者单位：University of Oxford; University of London; University College London
摘要：We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, non-positively curved square complexes. We deduce that many other properties of groups are undecidable. For hyperbolic groups, there cannot exist algorithms to determine largeness, the existence of a linear representation with infinite image (over any infinite field), or the rank of...
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作者：Willwacher, Thomas
作者单位：University of Zurich
摘要：We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmuller Lie algebra . The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by , up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) operads may be expressed through the cohomology ...
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作者：Beresnevich, Victor
作者单位：University of York - UK
摘要：This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of the sets of weighted badly approximable points. The problems have been recently settled in dimension two but remain open in higher dimensions. In this paper we develop new techniques that allow us to tackle them in full generality. The techniques rest on latti...
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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：Bourgeois, Frederic; Oancea, Alexandru
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
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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...
