Characterization of the Hilbert ball by its automorphism group

Kang-Tae Kim; Steven G. Krantz

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Characterization of the Hilbert ball by its automorphism group

Kang-Tae Kim·Steven G. Krantz

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Abstract

Let $Ω$ be a bounded, convex domain in a separable Hilbert space. The authors prove a version of the theorem of Bun Wong, which asserts that if such a domain admits an automorphism orbit accumulating at a strongly pseudoconvex boundary point then it is biholomorphic to the ball. Key ingredients in the proof are a new localization argument using holomorphic peaking functions and the use of new ``normal families'' arguments in the construction of the limit biholomorphism.

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Kang-Tae Kim, Steven G. Krantz. 2001-06-03. Characterization of the Hilbert ball by its automorphism group. https://arxiv.org/abs/math/0106015

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