A metric analogue of Hartogs’ theorem

In this paper we prove a metric version of Hartogs’ theorem where the holomorphic function is replaced by a locally symmetric Hermitian metric. As an application, we prove that if the Kobayashi metric on a strongly pseudoconvex domain with C 2 smooth boundary is a Kähler metric, then the universal c...

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Published inGeometric and functional analysis Vol. 32; no. 5; pp. 1041 - 1062
Main Authors Gaussier, Hervé, Zimmer, Andrew
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2022
Springer Nature B.V
Subjects
Analysis
Analytic functions
Domains
Mathematics
Mathematics and Statistics
Smooth boundaries
Theorems
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Summary:In this paper we prove a metric version of Hartogs’ theorem where the holomorphic function is replaced by a locally symmetric Hermitian metric. As an application, we prove that if the Kobayashi metric on a strongly pseudoconvex domain with C 2 smooth boundary is a Kähler metric, then the universal cover of the domain is the unit ball.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-022-00615-6