Communications in Analysis and Geometry

Volume 25 (2017)

Number 4

A Schwarz-type lemma for noncompact manifolds with boundary and geometric applications

Pages: 719 – 749

DOI: https://dx.doi.org/10.4310/CAG.2017.v25.n4.a1

Authors

Guglielmo Albanese (Dipartimento di Matematica, Università degli Studi di Milano, Italy)

Marco Rigoli (Dipartimento di Matematica, Università degli Studi di Milano, Italy; and Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, Brazil)

Abstract

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.

Keywords

Liouville theorems, Schwarz lemma, Weak maximum principle

2010 Mathematics Subject Classification

35B53, 53A30, 53C21, 53C24, 58J05

Full Text (PDF format)

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