This analysis presents length-extremals and conjugate points in free step-2 rank-4 Carnot groups, highlighting cut-locus implications.
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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Montanari et al. (2025) studied this question.
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