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作者：Brown, Aaron; Hertz, Federico Rodriguez; Wang, Zhiren
摘要：In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices. Suppose Gamma is a lattice in a semisimple Lie group, all of whose factors have rank 2 or higher. Let a be alpha smooth Gamma-action on a compact nilmanifold M that lifts to an action on the universal cover. If the linear data rho of alpha contains a hyperbolic element, then there is a continuous semiconjugacy intertwining the actions of alpha and rho on a finite-index subgroup of Gamma. If alpha i...
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作者：Abert, Miklos; Bergeron, Nicolas; Biringer, Ian; Gelander, Tsachik; Nikolov, Nikolay; Raimbault, Jean; Samet, Iddo
摘要：We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge-Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini-Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the pos...
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作者：Birman, Joan S.; Hilden, Hugh M.
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作者：Du, Xiumin; Guth, Larry; Li, Xiaochun
摘要：We show that lim(t -> 0) e(it Delta) f(x) = f(x) almost every where for all f is an element of H-s (R-2) provided that s > 1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.
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作者：Marks, Andrew S.; Unger, Spencer T.
摘要：We give a completely constructive solution to Tarski's circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If k >= 1 and A, B subset of R-k are bounded Borel sets with the same positive Lebesgue measure whose boundaries have upper Minkowski dimension less than k, then A and B are equidecomposable by translations using Borel pieces. This answers a question of Wagon. Our proof uses ideas from the study of flows in graphs, and a rec...
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作者：Klingler, Bruno
摘要：An affine manifold X in the sense of differential geometry is a differentiable manifold admitting an atlas of charts with value in an affine space, with locally constant affine change of coordinates. Equivalently, it is a manifold whose tangent bundle admits a flat torsion free connection. Around 1955 Chern conjectured that the Euler characteristic of any compact affine manifold has to vanish. In this paper we prove Chern's conjecture in the case where X moreover admits a parallel volume form.
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作者：Cohn, Henry; Kumar, Abhinav; Miller, Stephen D.; Radchenko, Danylo; Viazovska, Maryna
摘要：Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.
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作者：Foscolo, Lorenzo; Haskins, Mark
摘要：There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kahler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G(2) : the metric cone over a Riemannian 6-manifold M has holonomy contained in G(2) if and only ...
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作者：Calabri, A.; Ciliberto, C.; Flamini, F.; Miranda, R.
摘要：We correct an error in the Multiple Point Formula (7.3) in the paper mentioned in the title. This correction propagates to formulas (7.5), (7.6), (7.23) and (8.18), and it affects minor results in Section 8, where few statements require an extra assumption, but it does not affect the main results of Section 8.
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作者：Temkin, Michael
摘要：We strengthen Gabber's l'-alteration theorem by avoiding all primes invertible on a scheme. In particular, we prove that any scheme X of finite type over a quasi-excellent threefold can be desingularized by a char(X)alteration, i.e., an alteration whose order is only divisible by primes noninvertible on X. The main new ingredient in the proof is a tame distillation theorem asserting that, after enlarging, any alteration of X can be split into a composition of a tame Galois alteration and a cha...
