Martin boundary of unlimited covering surfaces |
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Authors: | Hiroaki Masaoka Shigeo Segawa |
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Affiliation: | (1) Department of Mathematics Faculty of Science, Kytot Sangyo University, Kamigamo-Motoyama, Kitaku, 603 Kyoto, Japan;(2) Department of Mathematics, Daido Institute of Technology, 457-8530 Nagoya, Japan |
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Abstract: | LetW be an open Riemann surface and ap-sheeted (1<p<∞) unlimited covering surface ofW. Denote by Δ1 (resp., ) the minimal Martin boundary ofW (resp., ). For ζ ∈ Δ, let ζ be the (cardinal) number of the set of pionts which lie over ζ and the class of open connected subsetsM ofW such thatM∪{ζ} is a minimal fine neighborhood of ζ. Our main result is the following: , where is the number of components of π-1 M and π is the projection of ontoW. Moreover, some applications of the above results are discussed whenW is the unit disc. |
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