ON THE CHARACTERIZATION OF A RIEMANN SURFACE BY ITS SEMIGROUP OF ENDOMORPHISMS

Authors
EREMENKO A
Citation
A. Eremenko, ON THE CHARACTERIZATION OF A RIEMANN SURFACE BY ITS SEMIGROUP OF ENDOMORPHISMS, Transactions of the American Mathematical Society, 338(1), 1993, pp. 123-131
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
338
Issue
1
Year of publication
1993
Pages
123 - 131
Database
ISI
SICI code
0002-9947(1993)338:1<123:OTCOAR>2.0.ZU;2-F
Abstract
Suppose D1 and D2 be Riemann surfaces which have bounded nonconstant h olomorphic functions. Denote by E(D(i)), i = 1 , 2, the semigroups of all holomorphic endomorphisms. If phi: E(D1) --> E(D2) is an isomorphi sm of semigroups then there exists a conformal or anticonformal isomor phism psi: D1 --> D2 such that phi is the conjugation by psi. Also the semigroup of injective endomorphisms as well as some parabolic surfac es are considered.