Maps conjugating holomorphic maps in C^n

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If f is a bijection from C^n onto a complex manifold M, which conjugates every holomorphic map in C^n to an endomorphism in M, then we prove that f is necessarily biholomorphic or antibiholomorphic. This extends a result of A. Hinkkanen to higher dimensions. As a corollary, we prove that if there is an epimorphism from the semigroup of all holomorphic endomorphisms of C^n to the semigroup of holomorphic endomorphisms in M, or an epimorphism in the opposite direction for a doubly-transitive M, then it is given by conjugation by some biholomorphic or antibiholomorphic map. We show also that there are two unbounded domains in C^n with isomorphic endomorphism semigroups but which are neither biholomorphically nor antibiholomorphically equivalent.
10 pages

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Complex Variables, Dynamical Systems, 32H02; 32H50

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http://salesiana.dossiersoluciones.com/handle/123456789/66240

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0301120
 http://arxiv.org/abs/math/0301120

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arXiv