The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields

Yuting Wu; Chengyang Yi; Yu Zheng

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arXiv · 2409.08011

The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields

Yuting Wu·Chengyang Yi·Yu Zheng

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Abstract

We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly positive definite (0, 2)-tensor fields on compact submanifolds with or without boundary in Riemannian manifolds with nonnegative sectional curvature by the Alexandrov-Bakelman-Pucci (ABP) method. It should be a generalization of S. Brendle in [2].

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Yuting Wu, Chengyang Yi, Yu Zheng. 2024-09-12. The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields. https://arxiv.org/abs/2409.08011

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