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

TL;DR

This paper establishes a Schwarz-type lemma for noncompact manifolds with boundary, leveraging a weak maximum principle, and applies it to conformal deformations, extending classical results in geometric analysis.

Contribution

It introduces a new Schwarz-type lemma for noncompact manifolds with boundary and demonstrates its applications to conformal geometry, generalizing previous classical results.

Findings

Proves a Schwarz-type lemma for noncompact manifolds with boundary.

Develops a form of the weak maximum principle of independent interest.

Extends classical results in conformal geometry, including a generalization of Escobar's theorem.

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.