A Schwarz-type lemma for noncompact manifolds with boundary and   geometric applications
  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. 
Guglielmo Albanese and Marco Rigoli
math.DG math.AP