Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary

Qianqiao Guo, Fengbo Hang, Xiaodong Wang

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)1419-1439
Number of pages21
JournalMathematical Research Letters
Volume28
Issue number5
DOIs
StatePublished - 2021

ASJC Scopus subject areas

  • General Mathematics

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