Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary
Qianqiao Guo, Fengbo Hang, Xiaodong Wang · arXiv (Cornell University) · 2019
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.