On the Growth of the Bergman Metric Near a Point of Infinite Type

Bharali, G (2020) On the Growth of the Bergman Metric Near a Point of Infinite Type. In: Journal of Geometric Analysis .

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Abstract

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in C2 near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints�some of them necessary for a non-trivial Bergman space. However, these are mild constraints: unlike most earlier works on this subject, we are able to make estimates for non-convex pseudoconvex models as well. In fact, the domains we can analyse range from being mildly infinite-type to very flat at infinite-type boundary points.

Item Type:	Journal Article
Publication:	Journal of Geometric Analysis
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer
Keywords:	Bergman kernel; Bergman metric; Bergman–Fuchs formulas; Infinite type; Optimal estimates
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	22 Jan 2020 09:28
Last Modified:	22 Jan 2020 09:28
URI:	http://eprints.iisc.ac.in/id/eprint/64363

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