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arXiv · 2503.00021

New properties of length-extremals in free step-2 rank-4 Carnot groups

Annamaria Montanari·Daniele Morbidelli
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Abstract

In the free, step-2, rank-4 sub-Riemannian Carnot group, we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut-locus of the origin. Finally, we give some upper estimates for the cut-time of extremals.

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Annamaria Montanari, Daniele Morbidelli. 2026-01-24. New properties of length-extremals in free step-2 rank-4 Carnot groups. https://arxiv.org/abs/2503.00021

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