4 papers · 1 filter
Quasihyperbolic domains are CAT(2)
Toni Ikonen, Abhishek Pandey
We prove that every proper subdomain of the Euclidean space equipped with its quasihyperbolic metric is CAT(2). The CAT property leads to a positive resolution of Väisälä's uniquen…
A rescaling principle for quasiregular curves with applications to hyperbolicity
Toni Ikonen, Jonathan Pim
We prove a Miniowitz--Zalcman rescaling principle for quasiregular curves into calibrated manifolds. We have two main applications. First, we introduce Brody hyperbolicity adapted…
Sobolev-to-Lipschitz property of geodesically complete spaces with curvature bounded from above
Emanuele Caputo, Nicola Cavallucci, Toni Ikonen
We prove that every length space with curvature bounded from above that is geodesically complete has the Sobolev-to-Lipschitz property with exponent infinity. That is, every Sobole…
Ultralimits of Sobolev maps and stability of Dehn functions
Toni Ikonen, Stefan Wenger
We show that the ultralimit of a bounded sequence of Lipschitz maps into pointed metric spaces extends naturally to -bounded sequences of Sobolev maps and that this ultralimit f…