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.
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