Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions
Differential Geometry
2015-06-16 v1 Metric Geometry
Optimization and Control
Abstract
In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Euclidean rectifiability.
Cite
@article{arxiv.1506.04339,
title = {Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions},
author = {Davide Barilari and Ugo Boscain and Enrico Le Donne and Mario Sigalotti},
journal= {arXiv preprint arXiv:1506.04339},
year = {2015}
}
Comments
24 pages, 17 figures