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Conformal embeddings of an open Riemann surface into another – a counterpart of univalent function theory. (English) Zbl 1456.30080

Summary: We study conformal embeddings of a noncompact Riemann surface of finite genus into compact Riemann surfaces of the same genus and show some of the close relationships between the classical theory of univalent functions and our results. Some new problems are also discussed. This article partially intends to introduce our results and to invite the function-theorists on plane domains to the topics on Riemann surfaces.

MSC:

30F99 Riemann surfaces
30C55 General theory of univalent and multivalent functions of one complex variable
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