Communications in Analysis and Geometry
Volume 25 (2017)
A Schwarz-type lemma for noncompact manifolds with boundary and geometric applications
Pages: 719 – 749
We prove a Schwarz-type lemma for noncompact manifolds with possibly noncompact boundary. The result is a consequence of a suitable form of the weak maximum principle of independent interest. The paper is enriched with applications to conformal deformations of noncompact manifolds with boundary, among them a generalization of a classical result by Escobar.
Liouville theorems, Schwarz lemma, Weak maximum principle
2010 Mathematics Subject Classification
35B53, 53A30, 53C21, 53C24, 58J05
The authors thank the Departamento de Matemáticas of the Universidad de Murcia, where part of this paper has been written, for the warm hospitality. G .A. also thanks Lucio Mari for many fruitful discussions.
Received 12 June 2015
Published 1 November 2017