Calculus of Variations and Geometric Measure Theory
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D. Barilari - U. Boscain - E. Le Donne - M. Sigalotti

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

created by barilari on 13 Jun 2015
modified on 08 Oct 2016

[BibTeX]

Published Paper

Inserted: 13 jun 2015
Last Updated: 8 oct 2016

Journal: Journal of Dynamical and Control Systems
Year: 2016

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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