59 citations · 65 across the 3 of their papers we have counts for
7 papers
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…
Cut time in the sub-Riemannian problem on the Cartan group
Andrei Ardentov, Eero Hakavuori
We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachko…
Gradings for nilpotent Lie algebras
Eero Hakavuori, Ville Kivioja, Terhi Moisala +1
We present a constructive approach to torsion-free gradings of Lie algebras. Our main result is the computation of a maximal grading. Given a Lie algebra, using its maximal grading…
ODE trajectories as abnormal curves in Carnot groups
Eero Hakavuori
We prove that for every polynomial ODE there exists a Carnot group where the trajectories of the ODE lift to abnormal curves. The proof defines an explicit construction to determin…
Infinite geodesics and isometric embeddings in Carnot groups of step 2
Eero Hakavuori
In the setting of step 2 sub-Finsler Carnot groups with strictly convex norms, we prove that all infinite geodesics are lines. It follows that for any other homogeneous distance, a…
Blowups and blowdowns of geodesics in Carnot groups
Eero Hakavuori, Enrico Le Donne
This paper provides some partial regularity results for geodesics (i.e., isometric images of intervals) in arbitrary sub-Riemannian and sub-Finsler manifolds. Our strategy is to st…
Non-minimality of corners in subriemannian geometry
Eero Hakavuori, Enrico Le Donne
We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result…