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

2025/02/23 by Annamaria Montanari, Montanari, Annamaria, Daniele Morbidelli +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2503.00021

openalex publication_date 2025/02/23 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

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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