A metric analogue of Hartogs' theorem

2021/11/23 by Hervé Gaussier, Gaussier, Hervé, Andrew Zimmer +1 · 2 citations
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2111.12029

openalex publication_date 2021/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C² smooth boundary is a Kähler metric, then the universal cover of the domain is the unit ball.

Cited by

• On Point Separation of Bergman Space on Stein Manifolds with Constant Holomorphic Sectional Curvature
• Kahlerity of invariant metrics on pseudoconvex domain of dimension two

Related

• The equivalent classical metrics on the Cartan-Hartogs Domains
• Canonical metrics on Hartogs domains
• Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric
• Kähler geometry of bounded pseudoconvex Hartogs domains
• A Kobayashi metric version of Bun Wong's theorem