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作者：Meeks, William H., III; Mira, Pablo; Perez, Joaquin; Ros, Antonio
作者单位：University of Massachusetts System; University of Massachusetts Amherst; Universidad Politecnica de Cartagena; University of Granada; University of Granada
摘要：We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.
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作者：Kang, Moon-Jin; Vasseur, Alexis F.
作者单位：Korea Advanced Institute of Science & Technology (KAIST); University of Texas System; University of Texas Austin
摘要：We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the vanishing viscosity limit, we show a contraction property for any large perturbations of viscous shocks to the Navier-Stokes system. The contraction estimate does not depend on the strength of the viscosity. This provides a good control on the inviscid limit process. We prove that, for any initial...
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作者：Petersen, Peter; Wink, Matthias
作者单位：University of California System; University of California Los Angeles
摘要：We show that manifolds with [n/2]-positive curvature operators are rational homology spheres. This follows from a more general vanishing and estimation theorem for the pth Betti number of closed n-dimensional Riemannian manifolds with a lower bound on the average of the lowest n - p eigenvalues of the curvature operator. This generalizes results due to D. Meyer, Gallot-Meyer, and Gallot.
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作者：Orponen, Tuomas
作者单位：University of Jyvaskyla
摘要：I prove that closed n-regular sets E subset of R-d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.
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作者：Eilat, Matan; Klartag, Bo'az
作者单位：Weizmann Institute of Science
摘要：Let M be a complete, connected Riemannian surface and suppose that S subset of M is a discrete subset. What can we learn about M from the knowledge of all Riemannian distances between pairs of points of S? We prove that if the distances in S correspond to the distances in a 2-dimensional lattice, or more generally in an arbitrary net in R-2, then M is isometric to the Euclidean plane. We thus find that Riemannian embeddings of certain discrete metric spaces are rather rigid. A corollary is tha...
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作者：Klingler, B.; Otwinowska, A.
作者单位：Humboldt University of Berlin
摘要：Given V a polarizable variation of Z-Hodge structures on a smooth connected complex quasi-projective variety S, the Hodge locus for V-circle times is the set of closed points s of S where the fiber V-s has more Hodge tensors than the very general one. A classical result of Cattani, Deligne and Kaplan states that the Hodge locus for V-circle times is a countable union of closed irreducible algebraic subvarieties of S, called the special subvarieties of S for V. Under the assumption that the adj...
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作者：Buckmaster, T.; Germain, P.; Hani, Z.; Shatah, J.
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：Consider the cubic nonlinear Schrodinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.
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作者：Hubner, Katharina; Schmidt, Alexander
作者单位：Hebrew University of Jerusalem; Ruprecht Karls University Heidelberg
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作者：Chen, Gao
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：In this paper, we prove that for any Kahler metrics omega(0) and chi on M, there exists a Kahler metric omega(phi) = omega(0) + root-1 partial derivative(partial derivative) over bar phi > 0 satisfying the J-equation tr omega(phi)chi = c if and only if (M, [omega(0)], [chi]) is uniformly J-stable. As a corollary, we find a sufficient condition for the existence of constant scalar curvature Kahler metrics with c(1) < 0. Using the same method, we also prove a similar result for the supercritical...
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作者：Chan, Kei Yuen
作者单位：Fudan University
摘要：Let F be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from GL(n+1)( F) to GL(n)( F). A main result shows that each Bernstein component of an irreducible smooth representation of GL(n+1)( F) restricted to GL(n)(F) is indecomposable. We also classify all irreducible representations which are projective when restricting from GL(n+1)( F) to GL(n)( F). A main tool of our study is a notion of left and right derivatives, ext...
