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

Yuting Wu; Chengyang Yi; Yu Zheng

paper

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

arXiv:2409.08011

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].

12 pages