Escape from compact sets of normal curves in subfinsler Carnot groups

\nIn 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 t1/s, where s denotes the step of the Carnot group. In particular, in subFinsler Carnot groups there are no periodic normal geodesics.\n

Publication Details

Journal
Springer Link (Chiba Institute of Technology)
Published
2024-10-25
DOI
https://doi.org/10.1051/cocv/2024067/pdf
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
Field-Weighted Citation Impact
0.00

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article

Escape from compact sets of normal curves in subfinsler Carnot groups

Springer Link (Chiba Institute of Technology)
Geometric Analysis and Curvature Flows
article

Escape from compact sets of normal curves in subfinsler Carnot groups

article en

Abstract

\nIn 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 t1/s, where s denotes the step of the Carnot group. In particular, in subFinsler Carnot groups there are no periodic normal geodesics.\n

Springer Link (Chiba Institute of Technology)
National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Openalex Percentile: Top 42%
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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Escape from compact sets of normal curves in subfinsler Carnot groups · Springer Link (Chiba Institute of Technology) (2024) | TGRS Research Map | TGRS