8 citations · 24 across the 15 of their papers we have counts for
16 papers
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…
Coarea Inequality for Monotone Functions on Metric Surfaces
Behnam Esmayli, Toni Ikonen, Kai Rajala
We study coarea inequalities for metric surfaces -- metric spaces that are topological surfaces, without boundary, and which have locally finite Hausdorff 2-measure …
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…
Energy estimates in sum-product and convexity problems
Akshat Mudgal
We prove a new class of low-energy decompositions which, amongst other consequences, imply that any finite set of integers may be written as , where and a…
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…
Duality of moduli in regular metric spaces
Atte Lohvansuu, Kai Rajala
F. Gehring and W. Ziemer proved that the p-modulus of the family of paths connecting two continua is dual to the p^*-modulus of the corresponding family of separating hypersurfaces…