Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions |
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| Authors: | Davide Barilari Ugo Boscain Enrico Le Donne Mario Sigalotti |
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| Affiliation: | 1.IMJ-PRG,Université Paris Diderot, UMR CNRS 7586 - UFR de Mathématiques,Paris,France;2.CNRS, CMAP, école Polytechnique,Université Paris-Saclay, Team GECOInria,Palaiseau,France;3.Department of Mathematics and Statistics,University of Jyv?skyl?,Jyv?skyl?,Finland;4.Inria, team GECO & CMAP, école Polytechnique, CNRS,Université Paris-Saclay,Palaiseau,France |
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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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