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arXiv · 1506.04339

Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions

Davide Barilari·Ugo Boscain·Enrico Le Donne·Mario Sigalotti
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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.

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Davide Barilari, Ugo Boscain, Enrico Le Donne, Mario Sigalotti. 2015-06-14. Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions. https://arxiv.org/abs/1506.04339

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