Characterization of \bf Cⁿ by its automorphism group

2000/08/25 by Alexander Isaev, Isaev, Alexander
Mathematics · #32M05 #32M17 #32Q57 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32M05 #msc:32M17 #msc:32Q57

paper · pdf · doi:10.48550/arxiv.math/0008193

to appear in Proc. Steklov Inst. math

arxiv created 2000/08/25 · openalex publication_date 2000/08/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if the group of holomorphic automorphisms of a connected Stein manifold M is isomorphic to that of \bf Cⁿ as a topological group equipped with the compact-open topology, then M is biholomorphically equivalent to \bf Cⁿ.

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