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Characterization of ${\bf C}^n$ by its automorphism group

Alexander Isaev
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Abstract

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

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Alexander Isaev. 2000-08-25. Characterization of ${\bf C}^n$ by its automorphism group. https://arxiv.org/abs/math/0008193

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