Dimitrios Ntalampekos

Rigidity theorems for circle domains

A circle domain Ω in the Riemann sphere is a domain each of whose boundary components is either a circle or a point. A circle domain Ω is called conformally rigid if every conformal map from Ω onto another circle domain is the restriction of a Möbius transformation. In this talk I will present some new rigidity theorems for circle domains satisfying a certain quasihyperbolic condition. As a corollary, John and Hölder circle domains are rigid. This provides new evidence for a conjecture of He and Schramm, relating rigidity and conformal removability. This talk is based on joint work with Malik Younsi.