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math.DG2026
A comparison theorem with applications to sharp geometric inequalities for submanifolds
Shengliang Pan, Chengyang Yi
The authors derive an explicit formula for the Jacobian determinant of the normal exponential map on a submanifold, use it to prove a new comparison theorem related to Heintze‑Karc…
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…