On the number of holomorphic mappings between Riemann surfaces of finite analytic type
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Published:2011-06-20
Issue:3
Volume:54
Page:711-730
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ISSN:0013-0915
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Container-title:Proceedings of the Edinburgh Mathematical Society
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language:en
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Short-container-title:Proceedings of the Edinburgh Mathematical Society
Author:
Imayoshi Yoichi,Ito Manabu,Yamamoto Hiroshi
Abstract
AbstractThe set of non-constant holomorphic mappings between two given compact Riemann surfaces of genus greater than 1 is always finite. This classical statement was made by de Franchis. Furthermore, bounds on the cardinality of the set depending only on the genera of the surfaces have been obtained by a number of mathematicians. The analysis is carried over in this paper to the case of Riemann surfaces of finite analytic type (i.e. compact Riemann surfaces minus a finite set of points) so that the finiteness result, together with a crude but explicit bound depending only on the topological data, may be extended for the number of holomorphic mappings between such surfaces.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics
Reference14 articles.
1. Beiträge zur Klassifizerung der Flächenabbildungen;Hopf;J. Reine Angew. Math.,1931
2. On holomorphic maps between Riemann surfaces of genera three and two;Mednykh;Dokl. Akad. Nauk SSSR,2009
3. Holomorphic mappings between compact Riemann surfaces
4. Riemann Surfaces