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

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.
Type de document :
Pré-publication, Document de travail
24 pages, 17 figures. 2015
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https://hal.inria.fr/hal-01164043
Contributeur : Mario Sigalotti <>
Soumis le : mardi 16 juin 2015 - 09:49:34
Dernière modification le : jeudi 10 mai 2018 - 02:05:34

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  • HAL Id : hal-01164043, version 1
  • ARXIV : 1506.04339

Citation

Davide Barilari, Ugo Boscain, Enrico Le Donne, Mario Sigalotti. Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions. 24 pages, 17 figures. 2015. 〈hal-01164043〉

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