On the existence of parabolic actions in convex domains of ℂk+1

We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact...

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Bibliographic Details
Published inCzechoslovak mathematical journal Vol. 65; no. 3; pp. 579 - 585
Main Authors Berteloot, François, Thu, Ninh Van
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2015
Subjects
Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
parabolic boundary point
32H50
convex domain
32M05
32H02
automorphism group
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Summary:We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric.
ISSN:0011-4642
1572-9141
DOI:10.1007/s10587-015-0197-y