7 papers · 1 filter
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…
Entire conformal curves are affine or have super-Euclidean energy growth
Toni Ikonen
We prove that entire conformal curves fall into two classes: either the curve is affine or the average energy in a ball is strictly increasi…
Smooth contact lifts to central extensions of Carnot groups
Eero Hakavuori, Susanna Heikkilä, Toni Ikonen
We consider the existence problem of lifting a smooth contact map between Carnot groups to a smooth contact map between central extensions of the original groups. Our main result i…
Quasiregular curves: Removability of singularities
Toni Ikonen
We prove a Painlevé theorem for bounded quasiregular curves in Euclidean spaces extending removability results for quasiregular mappings due to Iwaniec and Martin. The theorem is…