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.
A Schwarz-type lemma for noncompact manifolds with boundary and geometric applications / G. Albanese, M. Rigoli. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - 25:4(2017), pp. 719-749. [10.4310/CAG.2017.v25.n4.a1]
A Schwarz-type lemma for noncompact manifolds with boundary and geometric applications
G. Albanese;M. Rigoli
2017
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.
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