A metric analogue of Hartogs’ theorem

Abstract: In this talk I will discuss a version of Hartogs’ theorem where the holomorphic function is replaced by a locally symmetric Hermitian metric. As an application, I will explain how it implies the following rigidity result: if the Kobayashi metric on a strongly pseudoconvex domain is a K¨ahler metric, then the universal cover of the domain is biholomorphic to the unit ball. This is joint work with H. Gaussier.