Fridman's invariant, squeezing functions, and exhausting domains

Fusheng Deng; Xujun Zhang

Fridman's invariant, squeezing functions, and exhausting domains

Complex Variables 2018-11-06 v2

Authors: Fusheng Deng , Xujun Zhang

Abstract

We show that if a bounded domain $\Omega$ is exhausted by a bounded strictly pseudoconvex domain $D$ with $C^2$ boundary, then $\Omega$ 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

bounded domains pseudoconvex domains holomorphic dynamics

Cite

@article{arxiv.1810.12724,
  title  = {Fridman's invariant, squeezing functions, and exhausting domains},
  author = {Fusheng Deng and Xujun Zhang},
  journal= {arXiv preprint arXiv:1810.12724},
  year   = {2018}
}

Comments

A remark added in the end of the Introduction, and references are updated

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