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• A finite loop space not rationally equivalent to a compact Lie group AI翻译
  作者：Andersen, KKS; Bauer, T; Grodal, J; Pedersen, EK
  作者单位：Aarhus University; University of Munster; University of Chicago; State University of New York (SUNY) System; Binghamton University, SUNY
  摘要：We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.
• Recurrence and genericty AI翻译
  作者：Bonatti, C; Crovisier, S
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Bourgogne Europe
  摘要：We prove a C-1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C-1-generic diffeomorphisms. For instance, C-1-generic conservative diffeomorphisms (on connected manifolds) are transitive(1).
• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra AI翻译
  作者：Suter, R
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We describe the abelian ideals in b in a uniform way, that is, independent of the classification of complex simple Lie algebras. As an application we derive a formula for the maximal dimension of a commutative Lie subalgebra of g.
• Lattice point problems and values of quadratic forms AI翻译
  作者：Götze, F
  作者单位：University of Bielefeld
  摘要：For d-dimensional ellipsoids E with dgreater than or equal to5 we show that the number of lattice points in rE is approximated by the volume of rE, as r tends to infinity, up to an error of order O(r(d-2)) for general ellipsoids and up to an error of order o(r(d-2)) for irrational ones. The estimate refines earlier bounds of the same order for dimensions dgreater than or equal to9. As an application a conjecture of Davenport and Lewis about the shrinking of gaps between large consecutive value...
• The geometric complexity of special Lagrangian T2-cones AI翻译
  作者：Haskins, M
  作者单位：Johns Hopkins University
  摘要：We prove a number of results on the geometric complexity of special Lagrangian (SLG) T-2-cones in C-3. Every SLG T-2-cone has a fundamental integer invariant, its spectral curve genus. We prove that the spectral curve genus of an SLG T-2-cone gives a lower bound for its geometric complexity, i.e. the area, the stability index and the Legendrian index of any SLG T-2-cone are all bounded below by explicit linearly growing functions of the spectral curve genus. We prove that the cone on the Cliff...
• The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels AI翻译
  作者：Golse, F; Saint-Raymond, L
  作者单位：Institut Universitaire de France; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
  摘要：The present work establishes a Navier-Stokes limit for the Boltzmann equation considered over the infinite spatial domain R-3. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations whose limit points (in the w-L-1 topology) are governed by Leray solutions of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. Pure Appl. Math. 46(5), 667-753 (1993)] for the steady case, and in Lions-Masmoudi [Arch. ...
• Asymptotic analysis of Θ-hypergeometric functions AI翻译
  作者：Pasquale, A
  作者单位：TU Clausthal
  摘要：We define the Theta-hypergeometric functions as a generalization of the hypergeometric functions associated with root systems of Heckman and Opdam. In the geometric setting, the Theta-hypergeometric functions can be specialized to Harish-Chandra's spherical functions on Riemannian symmetric spaces of noncompact type, and also to the spherical functions on noncompactly causal symmetric spaces. After describing their regularity properties, we prove estimates for the Theta-hypergeometric function...
• Poincare series of a rational surface singularity AI翻译
  作者：Campillo, A; Delgado, F; Gusein-Zade, SM
  作者单位：Universidad de Valladolid; Lomonosov Moscow State University
• Singularity of mean curvature flow of Lagrangian submanifolds AI翻译
  作者：Chen, JY; Li, JY
  作者单位：University of British Columbia; Fudan University; Chinese Academy of Sciences
  摘要：In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Sigma(0) is Lagrangian and almost calibrated by Re Ohm in a Calabi-Yau n-fold (M, Ohm), and T > 0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature flow at a singular point (X-0, T) Is a stationary Lagrangian integer multiplicity current in R-2n with volume density greater than one at X-0. When n = 2, the ta...
• A stable cohomotopy refinement of Seiberg-Witten invariants: II AI翻译
  作者：Bauer, S
  作者单位：University of Bielefeld
  摘要：A gluing theorem for the stable cohomotopy invariant defined in the first article in this series of two gives new results on diffeomorphism types of decomposable manifolds.