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Fridman’s Invariant, Squeezing Functions, and Exhausting Domains

  • Fu Sheng DengEmail author
  • Xu Jun ZhangEmail author
Article
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Abstract

We show that if a bounded domain Ω is exhausted by a bounded strictly pseudoconvex domain D with C2 boundary, then Ω is holomorphically equivalent to D or the unit ball, and show that a bounded domain has to be holomorphically equivalent to the unit ball if its Fridman’s invariant has certain growth condition near the boundary.

Keywords

Squeezing function Fridman’s invariant exhausting domain 

MR(2010) Subject Classification

32H02 

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Notes

Acknowledgements

The first author thanks Professor John Erik Fornæss for discussions.

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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingP. R. China

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