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作者：Montgomery, Richard
作者单位：University of California System; University of California Santa Cruz
摘要：For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result for collinear instants (syzygies) in the zero angular momentum planar 3-body problem, and extends to thed + 1 body problem in d-space. The proof begins by identifying the translation-reduced configuration space with real dxd matrices, the degeneration locus...
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作者：Seward, Brandon
作者单位：New York University
摘要：For an ergodic p.m.p. action G?(X,) of a countable group G, we define the Rokhlin entropy hGRok(X,) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov-Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Under this analogy we prove that Krieger's finite generator theorem holds for all countably infinite groups. S...
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作者：Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; Garcia-Prada, Oscar; Gothen, Peter B.; Oliveira, Andre
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University System of Maryland; University of Maryland College Park; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidade do Porto; University of Tras-os-Montes & Alto Douro
摘要：Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli sp...
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作者：Benameur, Moulay-Tahar; Heitsch, James L.
作者单位：Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold admits no PSC metric; that any metric of PSC on such a foliation is bounded by a multiple of the reciprocal of the foliation K-area of the ambient manifold; and that Connes' van...
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作者：Barthel, Tobias; Hausmann, Markus; Naumann, Niko; Nikolaus, Thomas; Noel, Justin; Stapleton, Nathaniel
作者单位：University of Copenhagen; University of Regensburg; University of Munster; University of Kentucky
摘要：For a finite abelian group A, we determine the Balmer spectrum of SpA, the compact objects in genuine A-spectra. This generalizes the case A=Z/pZ due to Balmer and Sanders (Invent Math 208(1):283-326, 2017), by establishing (a corrected version of) their logp-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn's blue-shift theorem for Tate-constructions (Kuhn in Invent Math 157(2):345-370, 2004).
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作者：Avni, Nir; Lubotzky, Alexander; Meiri, Chen
作者单位：Northwestern University; Hebrew University of Jerusalem; Technion Israel Institute of Technology
摘要：If is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example SLn(Z), n3) and is a finitely generated group that is elementarily equivalent to , then is isomorphic to Gamma.
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作者：Figalli, Alessio; Serra, Joaquim
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In the classical obstacle problem, the free boundary can be decomposed into regular and singular points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139:155-184, 1977; J Fourier Anal Appl 4:383-402, 1998), regular points consist of smooth hypersurfaces, while singular points are contained in a stratified union of C1 manifolds of varying dimension. In two dimensions, this C1 result has been improved to C1, by Weiss (Invent Math 138:23-50, 1999). In this paper we prove ...
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作者：Bakker, Benjamin; Tsimerman, Jacob
作者单位：University System of Georgia; University of Georgia; University of Toronto
摘要：We extend the Ax-Schanuel theorem recently proven for Shimura varieties by Mok-Pila-Tsimerman to all varieties supporting a pure polarizable integral variation of Hodge structures. In fact, Hodge theory provides a number of conceptual simplifications to the argument. The essential new ingredient is a volume bound for Griffiths transverse subvarieties of period domains.
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作者：Bridgeland, Tom
作者单位：University of Sheffield
摘要：We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections with Gromov-Witten theory and exact WKB analysis.
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作者：Brendle, Simon; Choi, Kyeongsu
作者单位：Columbia University; Massachusetts Institute of Technology (MIT)
摘要：A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are -noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in R3, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in R3 which is strictly convex and noncollapsed.
