The complex geometry of Teichmüller spaces and bounded symmetric domains

Abstract

We study isometric maps between Teichmüller spaces and bounded symmetric domains in their intrinsic Kobayashi metric. From a complex analytic perspective, these two important classes of geometric spaces have several features in common but also exhibit many differences. The focus here is on recent results proved by the author; we give a list of open questions at the end. Paper based on plenary talk presented to the 6th Ahlfors-Bers Colloquium at Yale, 23-26 October 2014.

15 pages, 2 figures. Paper based on plenary talk presented to the 6th Ahlfors-Bers Colloquium at Yale, 23-26 October 2014; the talk is available to watch at the following URL https://www.youtube.com/watch?v=fT9hfq5ojU4