Computational Methods and Function Theory 3 (2003), No. 1, 253--272
Copyright Heldermann Verlag 2003
Joan J. Carmona
jcar@mat.uab.es, Departament de Matemátiques, Universitat Autónoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
Christian Pommerenke
pommeren@math.tu-berlin.de, Technische Universität, Fachbereich Mathematik, 10623 Berlin, Germany.
Let $f$ map the unit disk onto a simply connected domain $G$. In this paper we consider decompositions of the form $\partial G = C_1\cup \cdots\cup C_m$, in particular the case where $C_j$ are continua and we investigate inclusions between the cluster sets $I(f, \zeta)$, $I^{\pm}(f,\zeta)$, $\Pi(f,\zeta)$ and the given sets $C_j$. In this context the concept of a indecomposable continuum appears in a natural way.
Keywords: Conformal maps, indecomposable continua, prime ends, separation by a continuum.
MSC 2000: 30C35.
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