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Uniformization of cofat domains on metric two-spheres
Chengxi Li, Kai Rajala
We extend \emph{Schramm's cofat uniformization theorem} to cofat domains on upper Ahlfors 2-regular metric two-spheres . Specifically, we show that if is a cofat do…
Rigid circle domains with non-removable boundaries
Kai Rajala
We give a negative answer to the rigidity conjecture of He and Schramm by constructing a rigid circle domain on the Riemann sphere with conformally non-removable boundary. Here…
Conformal Uniformization of Domains Bounded by Quasitripods
Behnam Esmayli, Kai Rajala
We prove Koebe's conjecture and a version of Schramm's cofat uniformization theorem for domains satisfying conditions involving quasitripods, i.e., quasisymmet…
Exhaustions of circle domains
Dimitrios Ntalampekos, Kai Rajala
Koebe's conjecture asserts that every domain in the Riemann sphere is conformally equivalent to a circle domain. We prove that every domain satisfying Koebe's conjecture admits…