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Narasimhan–Simha-type metrics on strongly pseudoconvex domains in

Borah, D and Verma, K (2022) Narasimhan–Simha-type metrics on strongly pseudoconvex domains in. In: Complex Variables and Elliptic Equations .

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Official URL: https://doi.org/10.1080/17476933.2022.2069758


For a bounded domain (Formula presented.), let (Formula presented.) denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on D that are square integrable with respect to the weight (Formula presented.), where (Formula presented.) is an integer. The corresponding weighted kernel (Formula presented.) transforms appropriately under biholomorphisms and hence produces an invariant Kähler metric on D. Thus, there is a hierarchy of such metrics starting with the classical Bergman metric that corresponds to the case d = 0. This note is an attempt to study this class of metrics in much the same way as the Bergman metric has been with a view towards identifying properties that are common to this family. When D is strongly pseudoconvex, the scaling principle is used to obtain the boundary asymptotics of these metrics and several invariants associated with them. It turns out that all these metrics are complete on strongly pseudoconvex domains. © 2022 Informa UK Limited, trading as Taylor & Francis Group.

Item Type: Journal Article
Publication: Complex Variables and Elliptic Equations
Publisher: Taylor and Francis Ltd.
Additional Information: The copyright for this article belongs to the Taylor and Francis Ltd.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 21 Jun 2022 10:00
Last Modified: 21 Jun 2022 10:00
URI: https://eprints.iisc.ac.in/id/eprint/73930

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