2019

Ardentov, Andrei A.; Le Donne, Enrico; Sachkov, Yuri L.

This paper is a continuation of the work by the same authors on the Cartan groupequipped with the sub-Finsler∞norm. We start by giving a detailed presentation of thestructure of bang-bang extremal trajectories. Then we prove upper bounds on the number ofswitchings 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 thatevery two points can be connected by a piecewise smooth minimizer, and we give a uniformbound on the number of such pieces.