Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains

Kar, D (2024) Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains. In: Bulletin des Sciences Mathematiques, 195 .

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Abstract

We establish geometric upper and lower estimates for the Carathéodory and Kobayashi-Eisenman volume elements on the class of non-degenerate convex domains, as well as on the more general class of non-degenerate C-convex domains. As a consequence, we obtain explicit universal lower bounds for the quotient invariant both on non-degenerate convex and C-convex domains. Here the bounds we derive, for the above mentioned classes in Cn, only depend on the dimension n for a fixed n�2. Finally, it is shown that the Bergman kernel is comparable with these volume elements up to small/large constants depending only on n. © 2024 Elsevier Masson SAS

Item Type:	Journal Article
Publication:	Bulletin des Sciences Mathematiques
Publisher:	Elsevier Masson s.r.l.
Additional Information:	The copyright for this article belongs to authors.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	16 Dec 2024 11:10
Last Modified:	16 Dec 2024 11:10
URI:	http://eprints.iisc.ac.in/id/eprint/85796

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