5 papers · 1 filter
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…
Liouville's theorem in calibrated geometries
Toni Ikonen, Pekka Pankka
We consider the following extension of the classical Liouville theorem: A calibration , where , has the Liouville property if a Sobolev mappin…