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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the characterization of a Riemann surface by its semigroup of endomorphisms


Author: A. Erëmenko
Journal: Trans. Amer. Math. Soc. 338 (1993), 123-131
MSC: Primary 30D05; Secondary 20M20, 30F20
MathSciNet review: 1106188
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Abstract: Suppose $ {D_1}$ and $ {D_2}$ be Riemann surfaces which have bounded nonconstant holomorphic functions. Denote by $ E({D_i})$, $ i = 1,2$, the semigroups of all holomorphic endomorphisms. If $ \phi :E({D_1}) \to E({D_2})$ is an isomorphism of semigroups then there exists a conformal or anticonformal isomorphism $ \psi :{D_1} \to {D_2}$ such that $ \phi $ is the conjugation by $ \psi $. Also the semigroup of injective endomorphisms as well as some parabolic surfaces are considered.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1106188-2
Keywords: Holomorphic endomorphism, fixed point, permutable functions, semigroup, Riemann surface
Article copyright: © Copyright 1993 American Mathematical Society