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

Autor:	Guo, Qianqiao, Hang, Fengbo, Wang, Xiaodong
Rok vydání:	2019
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: Final version; to appear in Math. Res. Letters
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1912.05574 Zobrazit plný text záznamu View this record from Arxiv