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On the compactness of isometry groups in complex analysis

Seshadri, Harish and Verma, Kaushal (2009) On the compactness of isometry groups in complex analysis. In: Complex Variables, 54 (3-4). pp. 387-399.

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Abstract

We prove that the group of continuous isometries for the Kobayashi or Caratheodory metrics of a strongly convex domain in C-n is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a continuous isometry between a strongly convex domain and the ball has to be biholomorphic or anti-biholomorphic. Combining this with a metric version of Pinchuk's rescaling technique gives the main result.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Taylor and Francis Group.
Keywords: isometry group; compactness; Kobayashi metric; Caratheacuteodory metric;biholomorphic mapping
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 12 Jul 2010 08:53
Last Modified: 12 Jul 2010 08:53
URI: http://eprints.iisc.ernet.in/id/eprint/29206

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