A metric analogue of Hartogs' theorem

DOI10.1007/S00039-022-00615-6arXiv2111.12029WikidataQ114231697 ScholiaQ114231697MaRDI QIDQ6383776

Publication date: 23 November 2021

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

m a t h c a l C^{2}

smooth boundary is a K"ahler metric, then the universal cover of the domain is the unit ball.

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Stein manifolds (32Q28) Strongly pseudoconvex domains (32T15)

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