English

The squeezing function: exact computations, optimal estimates, and a new application

Complex Variables 2023-11-07 v2 Differential Geometry

Abstract

We present a new application of the squeezing function sDs_D, using which one may detect when a given bounded pseudoconvex domain DCnD\varsubsetneq \mathbb{C}^n, n2n\geq 2, is not biholomorphic to any product domain. One of the ingredients used in establishing this result is also used to give an exact computation of the squeezing function (which is a constant) of any bounded symmetric domain. This extends a computation by Kubota to any Cartesian product of Cartan domains at least one of which is an exceptional domain. Our method circumvents any case-by-case analysis by rank and also provides optimal estimates for the squeezing functions of certain domains. Lastly, we identify a family of bounded domains that are holomorphic homogeneous regular.

Keywords

Cite

@article{arxiv.2305.11145,
  title  = {The squeezing function: exact computations, optimal estimates, and a new application},
  author = {Gautam Bharali and Diganta Borah and Sushil Gorai},
  journal= {arXiv preprint arXiv:2305.11145},
  year   = {2023}
}

Comments

18 pages, 1 figure. Several expository observations in Sections 1-3 and references added; typos in Section 7 corrected. This is not the final accepted version; the publishers of J. Geom. Anal. -- in which the article has appeared -- do not want the final accepted version to appear publicly during a certain period. The version of record is available online: DOI given somewhere on this page>>

R2 v1 2026-06-28T10:38:29.108Z