Title: Cut time in the sub-Riemannian problem on the Cartan group
Authors: Andrei Ardentov, Eero Hakavuori
Journal title: ESAIM: COCV
A. Ardentov, E. Hakavuori, Cut time in the sub-Riemannian problem on the Cartan group, ESAIM: Control, Optimisation and Calculus of Variations, Vol. 28, No. 12, 19 pages. (https://doi.org/10.1051/cocv/2022006)
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 Yu. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we obtain a comparison with the known cut times in the sub-Riemannian Engel group, and a sufficient (generic) condition for the uniqueness of the length minimizer between two points. Hence we reduce the optimal synthesis to solving a certain system of equations in elliptic functions.
ArXiv ID (ENG): 2107.06730