Infinite Dimensional Holomorphic Homogeneous Regular Domains

  • Cho-Ho ChuEmail author
  • Kang-Tae Kim
  • Sejun Kim


We extend the concept of a finite dimensional holomorphic homogeneous regular (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of holomorphy and determine completely the class of infinite dimensional bounded symmetric domains which are HHR. We compute the greatest lower bound of the squeezing function of all HHR bounded symmetric domains, including the two exceptional domains. We also show that uniformly elliptic domains in Hilbert spaces are HHR.


Holomorphic homogeneous regular manifold Squeezing function Bounded symmetric domain Pseudoconvex domain 

Mathematics Subject Classification

Primary 58B12 32H02 32M15 32T05 Secondary 17C65 32F45 



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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary, University of LondonLondonUK
  2. 2.Center for Geometry and its applications and Department of MathematicsPohang University of Science and TechnologyPohangSouth Korea

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