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arXiv · 1608.06431

On the subRiemannian cut locus in a model of free two-step Carnot group

Annamaria Montanari·Daniele Morbidelli
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Abstract

We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators. We also calculate explicitly the cut time of any extremal path and the distance from the origin of all points of the cut locus. Finally, by using the Hamiltonian approach, we show that the cut time of strictly normal extremal paths is a smooth explicit function of the initial velocity covector. Finally, using our previous results, we show that at any cut point the distance has a corner-like singularity.

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Annamaria Montanari, Daniele Morbidelli. 2016-08-23. On the subRiemannian cut locus in a model of free two-step Carnot group. https://doi.org/10.1007/s00526-017-1149-1

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