3 papers
math.OC2021
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…
math.DG2020
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…
math.MG2019
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…