Criteria for zero capacity of ideal boundary components of Riemannian spaces

Wellington Ham Ow

Vol. 23 (1967), No. 3, 591–595

DOI: 10.2140/pjm.1967.23.591

Abstract

Capacities of ideal boundary components of Riemannian spaces are introduced to measure their magnitude with respect to harmonic functions on the spaces. The main purpose of this paper is to find zero capacity criteria.

The modular criterion, well-known for Riemann surfaces, i.e. for 2-dimensional Riemannian spaces, is shown to be valid for general Riemannian spaces. The so-called metric criterion, however, brings forth entirely new aspects for higher dimensions.

Mathematical Subject Classification

Primary: 53.72

Milestones

Received: 30 January 1967

Published: 1 December 1967