Escape from compact sets of normal curves in Carnot groups

2023/04/06 by Enrico Le Donne, Donne, Enrico Le, Nicola Paddeu +1
Arts and Humanities · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Historical Studies and Socio-cultural Analysis #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2304.03205

openalex publication_date 2023/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, each such a curve leaves every compact set, quantitatively. Namely, the distance between the points at time 0 and time t grows at least of the order of t^1/s, where s denotes the step of the Carnot group. In particular, in subFinsler Carnot groups there are no periodic normal geodesics.

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