3 papers
math.DG2026
A modified Bakry-Émery criterion inequality and the monotonicity of the Tsallis entropy
Xiaohan Cai, Xiaodong Wang
The Bakry-Émery criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-Émery crit…
math.AP2025
Uniqueness results for positive harmonic functions on manifolds with nonnegative Ricci curvature and strictly convex boundary
Xiaohan Cai
We prove some Liouville-type theorems for positive harmonic functions on compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary, thereby confirm…
math.AP2025
A note on Wang's conjecture for harmonic functions with nonlinear boundary condition
Xiaohan Cai
We obtain some Liouville type theorems for positive harmonic functions on compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary and partially v…