Martin boundary of unlimited covering surfaces |
| |
Authors: | Hiroaki Masaoka Shigeo Segawa |
| |
Institution: | (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 |
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|