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作者：Luk, Jonathan; Speck, Jared
作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
摘要：We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple plane wave solutions, starting from smooth initial data, is stable under perturbations of the initial data that break the plane symmetry. Moreover, we provide a sharp asymptotic description of the singularity formation. The new feature of our work is that th...
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作者：Huang, Jingyin
作者单位：McGill University
摘要：Let G be a right-angled Artin group with defining graph and let H be a finitely generated group quasi-isometric to G. We show if G satisfies that (1) its outer automorphism group is finite; (2) does not contain any induced 4-cycles; (3) is star-rigid; then H is commensurable to G. We show condition (2) is sharp in the sense that if contains an induced 4-cycle, then there exists an H quasi-isometric to G but not commensurable to G. Moreover, one can drop condition (1) if H is a uniform lattice ...
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作者：Glasner, Eli
作者单位：Tel Aviv University
摘要：We use the structure theory of minimal dynamical systems to show that, for a general group Gamma, a tame, metric, minimal dynamical system (X, Gamma) has the following structure: [GRAPHICS] Here (i) (X) over tilde is a metric minimal and tame system (ii) eta is a strongly proximal extension, (iii) Y is a strongly proximal system, (iv) pi is a point distal and RIM extension with unique section, (v)theta, theta* and tau are almost one-to-one extensions, and (vi) sigma is an isometric extension. ...
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作者：Bishop, Christopher J.
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We construct a non-polynomial entire function whose Julia set has finite 1-dimensional spherical measure, and hence Hausdorff dimension 1. In 1975, Baker proved the dimension of such a Julia set must be at least 1, but whether this minimum could be attained has remained open until now. Our example also has packing dimension 1, and is the first transcendental Julia set known to have packing dimension strictly less than 2. It is also the first example with a multiply connected wandering domain w...
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作者：Deroin, Bertrand; Kleptsyn, Victor; Navas, Andres
作者单位：CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); CY Cergy Paris Universite; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universidad de Santiago de Chile
摘要：We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are only finitely many orbits of connected components of its complement. For the case of minimal actions, we show that if the underlying group is (algebraically) free, then the action is ergodic with respect to the Lebesgue measure. This provides first answers to q...
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作者：Kerz, Moritz; Strunk, Florian; Tamme, Georg
作者单位：University of Regensburg
摘要：We prove that algebraic K-theory satisfies 'pro-descent' for abstract blow-up squares of noetherian schemes. As an application we derive Weibel's conjecture on the vanishing of negative K-groups.
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作者：Litt, Daniel
作者单位：Columbia University
摘要：Let X be a normal algebraic variety over a finitely generated field k of characteristic zero, and let be a prime. Say that a continuous adic representation of et 1 (X k) is arithmetic if there exists a finite extension k of k, and a representation. of p et 1 (Xk ), with. a subquotient of. p1(Xk). We show that there exists an integer N = N(X) such that every nontrivial, semisimple arithmetic representation of p et 1 (X) is nontrivial mod N. As a corollary, we prove that any nontrivial - adic re...
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作者：Ciubotaru, Dan
作者单位：University of Oxford
摘要：We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. Moreover, we show that every irreducible smooth G-representation contains a rigid type. This is a generalization of the unitarity criterion of Barbasch and Moy for representations wi...
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作者：Le, Daniel; Le Hung, Bao V.; Levin, Brandon; Morra, Stefano
作者单位：University of Toronto; Institute for Advanced Study - USA; University of Arizona; Universite de Montpellier
摘要：We prove the weight part of Serre's conjecture in generic situations for forms of U(3) which are compact at infinity and split at places dividing p as conjectured by Herzig (Duke Math J 149(1):37-116, 2009). We also prove automorphy lifting theorems in dimension three. The key input is an explicit description of tamely potentially crystalline deformation rings with Hodge-Tate weights (2, 1, 0) for unramified combined with patching techniques. Our results show that the (geometric) Breuil-M,zard...
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作者：Ekholm, Tobias; Ng, Lenhard; Shende, Vivek
作者单位：Uppsala University; Royal Swedish Academy of Sciences; Mittag-Leffler Institute; Duke University; University of California System; University of California Berkeley
摘要：We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere, along with a product on a filtered part of this homology. As a corollary, we obtai...
