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. © 2016, Springer Science+Business Media New York.

Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions

Le Donne, E.;
2017-01-01

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. © 2016, Springer Science+Business Media New York.
2017
Barilari, D.; Boscain, U.; Le Donne, E.; Sigalotti, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/976111
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