Holomorphic Invariants of Bounded Domains

  • Fusheng Deng
  • Zhiwei Wang
  • Liyou ZhangEmail author
  • Xiangyu Zhou
Part of the following topical collections:
  1. Invariant Metrics, an Important Tool in Several Complex Variables


In this survey paper, we give a review of some recent developments on holomorphic invariants of bounded domains, which include squeezing functions, Fridman’s invariants, p-Bergman kernels, and spaces of \(L^p\) integrable holomorphic functions.


Squeezing function Fridman invariant p-Bergman kernel Plurisubharmonic variation 

Mathematics Subject Classification

32F45 32H02 



The authors thank the referee for drawing the references [40] and [3] to our attention. The first author is partially supported by the University of Chinese Academy of Sciences and by NSFC Grants. The second author was partially supported by the Fundamental Research Funds for the Central Universities and by the NSFC Grant NSFC-11701031. The third and fourth authors are partially supported by NSFC Grants.


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© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingPeople’s Republic of China
  3. 3.School of Mathematical SciencesCapital Normal UniversityBeijingPeople’s Republic of China
  4. 4.Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijingPeople’s Republic of China

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