The automorphism space ∑(G) of a domain without punctiform prime ends

被引：0

作者：

Lauf W. ^{[1
]}

Schmieder G. ^{[2
]}

Volynec I.A. ^{[2
]}

机构：

[1] Mathematisches Institut der Univeristät, Würzburg D-97074, Am Hubland

[2] Fachberich L-Mathematik, Universität Oldenburg, Oldenburg D-26111

来源：

The Journal of Geometric Analysis | 2000年 / 10卷 / 4期

关键词：

automorphism group; boundary behavior; complex approximation; conformal mapping; connectedness; prime ends; total disconnectedness;

D O I：

10.1007/BF02921993

中图分类号：

学科分类号：

摘要：

Let G ⊆ ℂ be a simply connected domain and let ∑ (G) be its group of conformal automorphisms with the topology of uniform chordal convergence on G. In 1984 Gaier raised the question whether the connectedness of the space ∑ (G) implies that the domain G has only punctiform prime ends. As a contribution to answering this question in this paper the authors use suitable spike Junctions to construct a bounded domain without any punctiform prime end such that its automorphism space ∑ (G) is not discrete, but totally disconnected. © 2000 Mathematica Josephina, Inc.

引用

页码：697 / 712

页数：15

共 39 条

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