Sobolev Inequalities in Manifolds with Nonnegative Curvature

被引：34

作者：

Brendle, Simon ^{[1
]}

机构：

[1] Columbia Univ, 2990 Broadway, New York, NY 10027 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2023年 / 76卷 / 09期

基金：

美国国家科学基金会;

关键词：

ISOPERIMETRIC-INEQUALITIES; SHARP;

D O I：

10.1002/cpa.22070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a sharp Sobolev inequality on manifolds with nonnegative Ricci curvature. Moreover, we prove a Michael-Simon inequality for submanifolds in manifolds with nonnegative sectional curvature. Both inequalities depend on the asymptotic volume ratio of the ambient manifold. (c) 2022 Wiley Periodicals LLC.

引用

收藏

页码：2192 / 2218

页数：27

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