# Equivalence of domains with isomorphic semigroups of endomorphisms

@inproceedings{Merenkov2001EquivalenceOD, title={Equivalence of domains with isomorphic semigroups of endomorphisms}, author={Sergei Merenkov}, year={2001} }

For two bounded domains Ω 1 , Ω 2 in C whose semigroups of analytic endomorphisms E(Ω 1 ), E(Ω 2 ) are isomorphic with an isomorphism φ: E(Ω 1 ) → E(Ω 2 ), Eremenko proved in 1993 that there exists a conformal or anticonformal map ψ: Ω 1 → Ω 2 such that φf = ψ o f o ψ -1 , for all f ∈ E(Ω 1 ). In the present paper we prove an analogue of this result for the case of bounded domains in C n .

## 5 Citations

### MAPS CONJUGATING HOLOMORPHIC MAPS IN C n

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- 2003

If ψ 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 ψ is necessarily biholomorphic or antibiholomorphic.…

### MAPS CONJUGATING HOLOMORPHIC MAPS IN C

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If ψ is a bijection from Cn onto a complex manifold M, which conjugates every holomorphic map in Cn to an endomorphism in M, then we prove that ψ is necessarily biholomorphic or antibiholomorphic.…

### Varieties Characterized by their Endomorphisms

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We show that two varieties X and Y with isomorphic endomorphism semigroups are isomorphic up to field automorphism if one of them is affine and contains a copy of the affine line. A holomorphic…

### Stein spaces characterized by their endomorphisms

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- 2011

Finite dimensional Stein spaces admitting a proper holomorphic embedding of the complex line are characterized, among all complex spaces, by their holomorphic endomorphism semigroup in the sense that…

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