2019

Ardentov, A. A.; Le Donne, E.; Sachkov, Yu. L.

We study a sub-Finsler geometric problem on the free nilpotent group of rank 2 and step 3. Such a group is also called the Cartan group and has a natural structure of Carnot group, which we metrize by considering the l∞ norm on its first layer. We adopt the point of view of time-optimal control theory. We characterize extremal curves via the Pontryagin maximum principle. We describe abnormal and singular arcs and construct the bang-bang flow.