8 citations · 24 across the 15 of their papers we have counts for
9 papers · 1 filter
Extremal length and duality
Kai Rajala
Classical extremal length (or conformal modulus) is a conformal invariant involving families of paths on the Riemann sphere. In ``Extremal length and functional completion'', Fugle…
Uniformization of planar domains by exhaustion
Kai Rajala
We study the method of finding conformal maps onto circle domains by approximating with finitely connected subdomains. Every domain admits exhaustions, i.e., in…
Quasisymmetric Koebe uniformization with weak metric doubling measures
Kai Rajala, Martti Rasimus
We give a characterization of metric spaces quasisymmetrically equivalent to a finitely connected circle domain. This result generalizes the uniformization of Ahlfors 2-regular spa…
Uniformization with infinitesimally metric measures
Kai Rajala, Martti Rasimus, Matthew Romney
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces homeomorphic to . Given a measure on such a space,…
Quasispheres and metric doubling measures
Atte Lohvansuu, Kai Rajala, Martti Rasimus
Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere is a quasisphere if and only if is linearly locally connected…
Uniformization of two-dimensional metric surfaces
Kai Rajala
We establish uniformization results for metric spaces that are homeomorphic to the euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric def…