Parabolic exhaustions for strictly convex domains
type: Item
instance of: scholarly article
title: Parabolic exhaustions for strictly convex domains
zbMATH Open document ID: 0581.32018
DOI: 10.1007/BF01174598
author: Giorgio Patrizio
published in: Manuscripta Mathematica
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155016
review text: Given \(D\subset {\mathbb{C}}^ n\) a strictly convex domain and \(p\in D\) any point, the author defines a quasi-strictly parabolic exhaustion \(\tau\) of D with center p. The construction uses essentially the work of \textit{L. Lempert} on the Kobayashi metric [see Bull. Soc. Math. Fr. 109, 427-474 (1981; Zbl 0492.32025)]. Then to D and p are associated in a canonical way a complete circular domain \(G\subset {\mathbb{C}}^ n\) and a homeomorphism \(h: \bar G\to \bar D\) such that \(h(0)=p\), called the circular representation. The main result is: The circular representation is biholomorphic iff the Monge-Ampère foliation induced by the quasi-strictly parabolic exhaustion \(\tau\) of D centered at p is holomorphic. As a consequence a characterisation of the strictly convex domains D biholomorphic to a circular domain or to a ball in terms of the properties of the automorphism group of D is obtained.
Mathematics Subject Classification ID: 32E05
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32E10
zbMATH DE Number: 3929427
zbMATH Keywords: strictly convex domain
zbMATH Keywords: quasi-strictly parabolic exhaustion
zbMATH Keywords: Kobayashi metric
zbMATH Keywords: circular domain
zbMATH Keywords: circular representation
zbMATH Keywords: Monge-Ampère foliation
reviewed by: Nicolae Mihalache
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3929427