Potential theory for manifolds with boundary and applications to controlled mean curvature graphs

Abstract

AbstractIn this paper we characterize the Neumann-parabolicity of manifolds with boundary in terms of a new form of the classical Ahlfors maximum principle and of a version of the so-called Kelvin–Nevanlinna–Royden criterion. The motivation underlying this study is to obtain new information on the geometry of graphs with prescribed mean curvature inside a Riemannian product of the type