Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary
Differential Geometry
2020-05-27 v3 Analysis of PDEs
Abstract
We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the first Steklov eigenvalue by Xia-Xiong and verifies partially a conjecture by the third author. As a consequence, we derive several sharp Sobolev trace inequalities on these manifolds.
Keywords
Cite
@article{arxiv.1912.05574,
title = {Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary},
author = {Qianqiao Guo and Fengbo Hang and Xiaodong Wang},
journal= {arXiv preprint arXiv:1912.05574},
year = {2020}
}
Comments
Final version; to appear in Math. Res. Letters