A metric analogue of Hartogs' theorem

Hervé Gaussier; Andrew Zimmer

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arXiv · 2111.12029

A metric analogue of Hartogs' theorem

Hervé Gaussier·Andrew Zimmer

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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 $\mathcal{C}^2$ smooth boundary is a K\"ahler metric, then the universal cover of the domain is the unit ball.

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Hervé Gaussier, Andrew Zimmer. 2021-11-23. A metric analogue of Hartogs' theorem. https://arxiv.org/abs/2111.12029

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