Abstract
We present a new application of the squeezing function \(s_D\), using which one may detect when a given bounded pseudoconvex domain \(D\varsubsetneq \mathbb {C}^n\), \(n\ge 2\), 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.
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Nikolov–Andreev study a formally larger family of \(\mathbb {C}\)-convex domains that includes certain unbounded domains, but the latter are biholomorphic to bounded domains via projective transformations.
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Acknowledgements
We are grateful to Ngaiming Mok for drawing our attention to the book [12], which proved to be very relevant to the work in the first half of this paper, and to Harald Upmeier for suggesting an approach to proving a conjecture (now Proposition 2.12). We are also grateful to the anonymous referee of this work for their helpful suggestions on our exposition. G. Bharali is supported by a DST-FIST grant (grant no. TPN-700661). D. Borah and S. Gorai are supported in part by an SERB grant (Grant No. CRG/2021/005884).
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Bharali, G., Borah, D. & Gorai, S. The Squeezing Function: Exact Computations, Optimal Estimates, and a New Application. J Geom Anal 33, 383 (2023). https://doi.org/10.1007/s12220-023-01439-y
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DOI: https://doi.org/10.1007/s12220-023-01439-y