Thursday 25 March 2021, 12:45-13:15 via zoom
Elefterios Soultanis (RU)
The Homotopic Plateau--Douglas problem
The Plateau-Douglas problem is an extension of the classical Plateau's problem. Given k disjoint Jordan curves in an ambient space, and a smooth surface M with k boundary components, it asks to find a (weakly conformal) map from M of minimal area, spanning the Jordan curves. The homotopic variant of this problem additionally prescribes some topological data of the map. In this talk I will briefly discuss different kinds of topological data, and how to prove existence of (conformal) minimizers relying only on the presence of a local quadratic isoperimetric inequality. This method is conceptually simpler and more robust, extending to many nonsmooth metric spaces such as Alexandrov spaces. Joint work with Stefan Wenger.