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Existence of Dirichlet finite harmonic measures on Euclidean balls

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466, Japan
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Divide the ideal boundary of a noncompact Riemannian manifold M into two parts δ0 and δ1 Viewing that M is surrounded by two conducting electrodes δ0 and δ1 we ask whether (M; δ0, δ1) functions as a condenser in the sense that the unit electrostatic potential difference between two electrodes is produced by putting a charge of finite energy on one electrode when the other is grounded. The generalized condenser problem asks whether there exists a subdivision δ0 ∪ δ1 of the ideal boundary of M such that (M; δ0, δ1 functions as a condenser.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 133 , March 1994 , pp. 85 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

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