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ON PRIME ENDS AND PLANE CONTINUA

Published online by Cambridge University Press:  24 March 2003

J. J. CARMONA  and
C. POMMERENKE
J. J. CARMONA
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, [email protected]
C. POMMERENKE
Affiliation:
MA 8-2, Institut für Mathematik, Technische Universität, D-10623 Berlin, [email protected]
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Abstract

Let $f$ be a conformal map of the unit disk ${\bb D}$ onto the domain $G \subset \hat{\bb C} = {\bb C} \cup \{\infty\}$ . We shall always use the spherical metric in $\hat{\bb C}$ .

Carathéodory [3] introduced the concept of a prime end of $G$ in order to describe the boundary behaviour of $f$ in geometric terms; see for example [6, Chapter 9] or [12, Section 2.4]. There is a bijective map $\hat{f}$ of ${\bb T} = \partial {\bb D}$ onto the set of prime ends of $G$ .

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 641 - 650
Copyright
© The London Mathematical Society, 2002

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Footnotes

Research partially supported by grants PB98-1242-C02-02 (Ministerio de Educatión y Cultura) and 2000-SGR-00059 (Generalitat de Catalunya).