Some Criteria of Capacitive Type of a Noncompact Riemannian Manifold

Abstract

A fairly general concept of an integral capacity on a Riemannian manifold is considered, which includes the concepts of capacity known for the geometric theory of functions such as the classical and conformal capacities. In terms of this general capacity, as in the case of the classical capacity, the concept of capacitive type of Riemannian manifold is defined. In this paper, we present some integral criteria of the capacitive type of a non-compact Riemannian manifold, which complement and, in certain cases, strengthen the known criteria of the classical capacitive type of a Riemannian manifold.