Inventiones mathematicae

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• 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...
• Boundary regularity for the Ricci equation, geometric convergence, and Gel-fand's inverse boundary problem AI翻译
  作者：Anderson, M; Katsuda, A; Kurylev, Y; Lassas, M; Taylor, M
  作者单位：State University of New York (SUNY) System; Stony Brook University; Okayama University; Loughborough University; Aalto University; University of North Carolina; University of North Carolina Chapel Hill
  摘要：This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz bound on the mean curvature of the boundary. The second is to establish geometric convergence of a (sub)sequence of manifolds with boundary with such geometrical bounds and also an upper bound on the diameter and a lower bound on injectivity and boundary inject...
• K(1)-local topological modular forms AI翻译
  作者：Laures, G
  作者单位：Ruprecht Karls University Heidelberg
  摘要：We construct the Witten orientation of the topological modular forms spectrum tmf in the K(1)-local setting by attaching E-infinity cells to the bordism theory MO(8). We also identify the KO-homology of tmf with the ring of divided congruences.
• 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.
• Holomorphic H-spherical distribution vectors in principal series representations AI翻译
  作者：Gindikin, S; Krötz, B; Olafsson, G
  作者单位：Rutgers University System; Rutgers University New Brunswick; University of Oregon; Louisiana State University System; Louisiana State University
  摘要：Let G/H be a semisimple symmetric space. The main tool to embed a principal series representation of G into L-2(G/H) are the H-invariant distribution vectors. If G/H is a non-compactly causal symmetric space, then G/H can be realized as a boundary component of the complex crown Xi. In this article we construct a minimal G-invariant subdomain Xi(H) of Xi with G/H as Shilov boundary. Let pi be a spherical principal series representation of G. We show that the space of H-invariant distribution ve...
• Chow rings of toric varieties defined by atomic lattices AI翻译
  作者：Feichtner, EM; Yuzvinsky, S
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oregon
  摘要：We study a graded algebra D = D(L, g) over Z defined by a finite lattice L and a subset g in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De Concini and Procesi [2]. Our main result is a representation of D, for an arbitrary atomic lattice L, as the Chow ring of a smooth toric variety that we construct from L and g. We describe this variety both by its fan and geometrically by a series of b...
• The cauchy problem for quasi-linear Schrodinger equations AI翻译
  作者：Kenig, CE; Ponce, G; Vega, L
  作者单位：University of Chicago; University of California System; University of California Santa Barbara; University of Basque Country
• Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varieties AI翻译
  作者：Mavlyutov, AR
  作者单位：Indiana University System; Indiana University Bloomington
  摘要：One can deform the complex structure of Calabi-Yau hypersurfaces in toric varieties by changing the coefficients of the defining polynomial. However, there must also exist non-polynomial deformations of the Calabi-Yau hypersurfaces which cannot be realized inside the ambient toric variety. In this paper, we have constructed the missing non-polynomial deformations, which are induced by an automorphism on the open part of the ambient toric variety.
• Worn stones with flat sides all time regularity of the interface AI翻译
  作者：Daskalopoulos, P; Lee, KA
  作者单位：Columbia University; Seoul National University (SNU)
  摘要：We study the all time regularity of the free-boundary problem associated to the deformation of a compact weakly convex surface Sigma in R-3, with a flat side, by its Gaussian Curvature. We show that under certain necessary regularity and non-degeneracy initial conditions the interface separating the flat from the strictly convex side, remains smooth on 0
• Harmonic analysis on the infinite symmetric group AI翻译
  作者：Kerov, S; Olshanski, G; Vershik, A
  作者单位：Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
  摘要：The infinite symmetric group S(infinity), whose elements are finite permutations of {1,2,3,...}, is a model example of a big group. By virtue of an old result of Murray-von Neumann, the one-sided regular representation of S(infinity) in the Hilbert space l(2)(S(infinity)) generates a type II1 von Neumann factor while the two-sided regular representation is irreducible. This shows that the conventional scheme of harmonic analysis is not applicable to S(infinity): for the former representation, ...