2 papers
math.DG2026
A comparison theorem with applications to sharp geometric inequalities for submanifolds
Shengliang Pan, Chengyang Yi
In this paper, we derive an explicit expression for the Jacobian determinant of the normal exponential map on a submanifold, establishing a relationship with its ambient counterpar…
math.DG2024
The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields
Yuting Wu, Chengyang Yi, Yu Zheng
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 m…