Some aspects of the Kobayashi and Caratheodory metrics on pseudoconvex domains

Mahajan, Prachi ; Verma, Kaushal (2012) Some aspects of the Kobayashi and Caratheodory metrics on pseudoconvex domains Journal of Geometric Analysis, 22 (2). pp. 491-560. ISSN 1050-6926

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Official URL: https://link.springer.com/article/10.1007/s12220-0...

Related URL: http://dx.doi.org/10.1007/s12220-010-9206-4

Abstract

The purpose of this article is to consider two themes, both of which emanate from and involve the Kobayashi and the Caratheodory metric. First, we study the biholomorphic invariant introduced by B. Fridman on strongly pseudoconvex domains, on weakly pseudoconvex domains of finite type in C2, and on convex finite type domains in Cn 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 C2 and convex finite type domains in Cn 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 C1-isometries of the Kobayashi and Caratheodory metrics on a smoothly bounded strongly pseudoconvex domain.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
Keywords:Kobayashi Metric; Caratheodory Metric; Fridman's Invariant; Scaling; Isometry
ID Code:108082
Deposited On:01 Feb 2018 11:28
Last Modified:01 Feb 2018 11:28

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