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作者：Brendle, Simon; Daskalopoulos, Panagiota; Sesum, Natasa
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：In this paper, we study the classification of kappa-noncollapsed ancient solutions to three-dimensional Ricci flow on S-3. We prove that such a solution is either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.
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作者：Huang, Jingyin; Osajda, Damian
作者单位：University System of Ohio; Ohio State University; University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with a convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor imp...
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作者：Cascini, Paolo; Spicer, Calum
作者单位：Imperial College London
摘要：We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a Q-factorial projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial fol...
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作者：Bell, Jason; Zelmanov, Efim
作者单位：University of Waterloo; University of California System; University of California San Diego
摘要：We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
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作者：Kemeny, Michael
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We introduce a relativization of the secant sheaves from Green and Lazarsfeld (A simple proof of Petri's theorem on canonical curves, Geometry Today, 1984) and Ein and Lazarsfeld (Inventiones Math 190:603-646, 2012) and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin's Theorem for general canonical curves. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. Sec...
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作者：Dougall, Rhiannon; Sharp, Richard
作者单位：University of Bristol; University of Warwick
摘要：The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric group extensions and of the authors on geodesic flows. Our main application is to growth rates of periodic orbits for covers of an Anosov flow: we reduce the problem of counting periodic orbits in an amenable cover X to counting in a maximal abelian subcover ...
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作者：Sheridan, Nick; Smith, Ivan
作者单位：University of Edinburgh; University of Cambridge
摘要：We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev-Borisov's 'dual reflexive Gorenstein cones' construction. In particular we prove HMS for all Greene-Plesser mirror pairs (i.e., Calabi-Yau hypersurfaces in quotients of weighted projective spaces). We also prove it for certain mirror Calabi-Yau complete intersections arising from Borisov's construction via dual nef partitions, and also for certain Calabi-Yau complete intersections which d...
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作者：Lewin, Mathieu; Nam, Phan Thanh; Rougerie, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; University of Munich; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP)
摘要：We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic quantum system converges to the Gibbs measure of a nonlinear Schrodinger-type classical field theory, in terms of partition functions and reduced density matrices. The Gibbs measure thus describes the behavior of the infinite Bose gas at criticality, that i...
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作者：Cavalletti, Fabio; Milman, Emanuel
作者单位：International School for Advanced Studies (SISSA); Technion Israel Institute of Technology
摘要：The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for ametric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition locally: an essentially non-branching metric-measure space (X, d, m) (so that (supp(m), d) is a length-space and m( X) < infinity) verifying the local Curvature-Dimension condition CDloc( K, N) with parameters K is an element of R and N is an element of(1, infin...
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作者：Girouard, Alexandre; Lagace, Jean
作者单位：Laval University; University of London; University College London
摘要：Using methods in the spirit of deterministic homogenisation theory we obtain convergence of the Steklov eigenvalues of a sequence of domains in a Riemannian manifold to weighted Laplace eigenvalues of that manifold. The domains are obtained by removing small geodesic balls that are asymptotically densely uniformly distributed as their radius tends to zero. We use this relationship to construct manifolds that have large Steklov eigenvalues. In dimension two, and with constant weight equal to 1,...
