Characterization of the Hilbert ball by its automorphism group

Kim, Kang-Tae; Krantz, Steven

doi:10.1090/S0002-9947-02-02895-7

Characterization of the Hilbert ball by its automorphism group

Authors: Kang-Tae Kim and Steven G. Krantz
Journal: Trans. Amer. Math. Soc. 354 (2002), 2797-2818
MSC (2000): Primary 32A07
DOI: https://doi.org/10.1090/S0002-9947-02-02895-7
Published electronically: February 12, 2002
MathSciNet review: 1895204
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Abstract: Let $\Omega$ 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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