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Journal of the London Mathematical Society 2002 66(3):641-650; doi:10.1112/S0024610702003587
© 2002 by London Mathematical Society
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© The London Mathematical Society

On Prime Ends and Plane Continua

J. J. Carmona and C. Pommerenke

Departament de Matemàtiques, Universitat Autònoma de Barcelona E-08193 Bellaterra, Spain, jcar{at}mat.uab.es
MA 8-2, Institut für Mathematik, Technische Universität D-10623 Berlin, Germany, pommeren{at}math.tu-berlin.de

Received 11 June 2001. Revision received 7 January 2002.

Let f be a conformal map of the unit disk D onto the domain G sub C = C{cup}{{infty}}. We shall always use the spherical metric in 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 Formula of T = {partial}D onto the set of prime ends of G.


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