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New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow
New logarithmic Sobolev inequalities ε-regularity theorem Ricci flow Differential Geometry
2012/5/24
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
Inegalite de Sobolev et volume asymptotique
Sobolev inequality volume growth locally conformally flat
2011/9/23
Abstract: A result of M. Ledoux is that a complete Riemannian manifold with non negative Ricci curvature satisfying the Euclidean Sobolev inequality is the Euclidean space. We present a shortcut of th...
Basic Riemannian Geometry and Sobolev Estimates used in Symplectic Topology
Basic Riemannian Geometry Sobolev Estimates used Symplectic Topology
2011/2/22
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace
theory that play a prominent role in analytic approaches to symplectic topology. These
include relations...
The inclusion relation between Sobolev and modulation spaces
inclusion relation Sobolev modulation spaces
2010/11/30
The inclusion relations between the Lp-Sobolev spaces and the modulation spaces is determined explicitly. As an application,mapping properties of unimodular Fourier multiplier ei|D|
between Lp-Sobol...
一个 Sobolev 不等式及其几何应用
2007/12/12
本文导出了一个用中曲率向量来表示 sobolev 常数的 sobolev 不等式.应用此不等式,证明了如果$S^n(1)$中 m 维极小子流形 M 的第二基本形式的$L^m$模小于某个只依赖 m、n 的常数,则 M 必为全测地的.本文还包括一个关于稳定性的结果.