The squeezing function: exact computations, optimal estimates, and a new application
Abstract
We present a new application of the squeezing function , using which one may detect when a given bounded pseudoconvex domain , , 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.
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>>