Some Aspects of the Kobayashi and Carath,odory Metrics on Pseudoconvex Domains

Mahajan, Prachi and Verma, Kaushal (2012) Some Aspects of the Kobayashi and Carath,odory Metrics on Pseudoconvex Domains. In: Journal of Geometric Analysis, 22 (2). pp. 491-560.

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Abstract

The purpose of this article is to consider two themes, both of which emanate from and involve the Kobayashi and the Carath,odory metric. First, we study the biholomorphic invariant introduced by B. Fridman on strongly pseudoconvex domains, on weakly pseudoconvex domains of finite type in C (2), and on convex finite type domains in C (n) using the scaling method. Applications include an alternate proof of the Wong-Rosay theorem, a characterization of analytic polyhedra with noncompact automorphism group when the orbit accumulates at a singular boundary point, and a description of the Kobayashi balls on weakly pseudoconvex domains of finite type in C (2) and convex finite type domains in C (n) in terms of Euclidean parameters. Second, a version of Vitushkin's theorem about the uniform extendability of a compact subgroup of automorphisms of a real analytic strongly pseudoconvex domain is proved for C (1)-isometries of the Kobayashi and Carath,odory metrics on a smoothly bounded strongly pseudoconvex domain.

Item Type:	Journal Article
Publication:	Journal of Geometric Analysis
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Kobayashi metric;Caratheodory metric;Fridman's invariant; Scaling;Isometry
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 Mar 2012 11:39
Last Modified:	29 Mar 2012 11:39
URI:	http://eprints.iisc.ac.in/id/eprint/44076

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