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math.DG2025
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…
math.MG2025
On infinity thick quasiconvexity and applications
Miguel García-Bravo, Toni Ikonen, Zheng Zhu
We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space has a Lipschitz representative. We prove that when…
math.DG2025
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…