Analysis Seminar: Invariant metrics

Abstract: An invariant metric is a metric that is invariant under biholomorphic mappings, and for which all holomorphic mappings are contractive. On bounded convex sets, a theorem of Lempert says that all such metrics coincide (and therefore equal the Caratheodory metric, which we will define). We will discuss subsets V of the polydisk with the property that their intrinsic Caratheodory metric agrees with the one inherited from the polydisk. This is the complex geometry analogue of looking at subsets of a Riemannian manifold that are totally geodesic.

Host: Alan Chang