EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 75(89), pp. 217–232 (2004)

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CONFORMAL MAPPING OF RIEMANN SURFACES AND THE CLASSICAL THEORY OF UNIVALENT FUNCTIONS

M. Shiba

Hiroshima University, Japan

Abstract: Analytic mappings between Riemann surfaces are very natural objects in complex analysis. Corresponding to the classical univalent functions we have the class of injective holomorphic mappings — i.e., conformal embeddings — of a Riemann surface into another. We find indeed a number of analogies between them. On the other hand, because of the non-planarity of the domain surface, we face some new problems which we have never encountered in the classical theory. We discuss various problems concerning the conformal embeddings.

Classification (MSC2000): 30F99, 30C35; 30C55; 30F25, 30F45, 14H55; 76M40

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Electronic fulltext finalized on: 27 Oct 2004. This page was last modified: 22 Feb 2005.

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