Geodesic
Conformal Mapping of Riemann Surfaces and the Classical Theory of Univalent Functions
Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 217 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 : 30F99 30C35 30C55 30F25 30F45 14H55 76M40
Keywords: inivalent function 
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     author = {M. Shiba},
     title = {Conformal {Mapping} of {Riemann} {Surfaces} and the {Classical} {Theory} of {Univalent} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {217 },
     year = {2004},
     volume = {_N_S_75},
     number = {89},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2004_N_S_75_89_a16/}
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M. Shiba. Conformal Mapping of Riemann Surfaces and the Classical Theory of Univalent Functions. Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 217 . http://geodesic.mathdoc.fr/item/PIM_2004_N_S_75_89_a16/