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An intrinsic characterization of the direct product of balls

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In this paper, we give a characterization of the direct product of balls by its holomorphic automorphism group. Using a result on the standardization of certain compact group actions on complex manifolds, we show that, for a connected Stein manifold M of dimension n, if its holomorphic automorphism group contains a topological subgroup that is isomorphic to the holomorphic automorphism group of the direct product B of balls in C-n, then M itself is biholomorphically equivalent to B.

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