Sobolev Inequalities in Manifolds with Nonnegative Curvature

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. © 2022 Wiley Periodica...

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Bibliographic Details
Published inCommunications on pure and applied mathematics Vol. 76; no. 9; pp. 2192 - 2218
Main Author Brendle, Simon
Format Journal Article
LanguageEnglish
Published Melbourne John Wiley & Sons Australia, Ltd 01.09.2023
John Wiley and Sons, Limited
Subjects
Curvature
Inequalities
Manifolds (mathematics)
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Summary: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. © 2022 Wiley Periodicals LLC.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.22070