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Sobolev inequalities in manifolds with nonnegative intermediate Ricci curvature

Hui MaJing Wu
Mar 2023
摘要
We prove Michael-Simon type Sobolev inequalities for $n$-dimensionalsubmanifolds in $(n+m)$-dimensional Riemannian manifolds with nonnegative$n$-th intermediate Ricci curvature by using the Alexandrov-Bakelman-Puccimethod. These inequalities extends Theorem 1.4 in Brendle's work\cite{Brendle22} and Theorem 1.5 in Dong-Lin-Lu's work \cite{DLL22} to the$n$-Ricci curvature setting. In particular, a simple application of theseinequalities gives rise to some isoperimetric inequalities for minimalsubmanifolds in Riemannian manifolds.
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