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Riemann Domains with Boundary of Capacity Zero

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Nagoya University
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The well-known Thullen-Remmert-Stein’s theorem ([9], [7]) asserts that, for a domain D in CN and an n-dimensional irreducible analytic set S in D, a purely n-dimensional analytic set A in D — S has an essential singularity at any point in 5 if A has at least one essential singularity in S. In [1], E. Bishop generalized this to the case that A has the boundary of capacity zero in his sense. Afterwards, in [8], W. Rothstein obtained more precise informations on the essential singularities of A under the assumption dim A = 1. The main purpose in this paper is to generalize these Rothstein’s results to the case of arbitrary dimensional analytic sets.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 44 , December 1971 , pp. 1 - 15
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

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