Uniformization of metric surfaces by solving Plateau’s problem

Damaris Meier, University of Fribourg
Fine Hall 322

In-Person Talk

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The classical uniformization theorem states that any simply connected Riemann surface is conformally equivalent to the unit disk, complex plane or Riemann sphere. The non-smooth uniformization problem now asks for the strongest possible extension after replacing smooth surfaces by metric spaces. On the way to answering this question in the setting of metric surfaces of locally finite area, we encounter the quasisymmetric and quasiconformal uniformization results of Bonk-Kleiner and Rajala, respectively. Moreover, we will outline how the solution of Plateau‘s problem can be used to provide a more general uniformization theorem. Based on joint work with Stefan Wenger.