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 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.
Original language | English (US) |
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Pages (from-to) | 1419-1439 |
Number of pages | 21 |
Journal | Mathematical Research Letters |
Volume | 28 |
Issue number | 5 |
DOIs | |
State | Published - 2021 |
ASJC Scopus subject areas
- General Mathematics