Enrico Le Donne
P.O. Box 35, FI-40014, Finland
Department of Mathematics and Statistics, University of Jyväskylä
Ardentov A. A., Le Donne E., Sachkov Y. L.
Sub-Finsler Geodesics on the Cartan Group
2019, vol. 24, no. 1, pp. 36-60
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.