Mathematical Research Letters
Volume 28 (2021)
Liouville-type theorems on manifolds with nonnegative curvature and strictly convex boundary
Pages: 1419 – 1439
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 for the first Steklov eigenvalue by Xia–Xiong and verifies partially a conjecture by the third named author. As a consequence, we derive several sharp Sobolev trace inequalities on such manifolds.
The third-named author is partially supported by Simons Foundation Collaboration Grant for Mathematicians #312820.
Received 8 January 2020
Accepted 25 May 2020
Published 16 August 2022