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

Abstract

We present a new application of the squeezing function $s_D$, using which one may detect when a given bounded pseudoconvex domain $D{\mathbb{C}}^n$, $n\ge 2$, 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.

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>>