Not all sub-Riemannian minimizing geodesics are smooth

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chitour, Yacine, Jean, Frédéric, Monti, Roberto, Rifford, Ludovic, Sacchelli, Ludovic, Sigalotti, Mario, Socionovo, Alessandro
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912212847689728
author Chitour, Yacine
Jean, Frédéric
Monti, Roberto
Rifford, Ludovic
Sacchelli, Ludovic
Sigalotti, Mario
Socionovo, Alessandro
author_facet Chitour, Yacine
Jean, Frédéric
Monti, Roberto
Rifford, Ludovic
Sacchelli, Ludovic
Sigalotti, Mario
Socionovo, Alessandro
contents A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an example of a $C^2$ but not $C^3$ length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure.
format Preprint
id arxiv_https___arxiv_org_abs_2501_18920
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Not all sub-Riemannian minimizing geodesics are smooth
Chitour, Yacine
Jean, Frédéric
Monti, Roberto
Rifford, Ludovic
Sacchelli, Ludovic
Sigalotti, Mario
Socionovo, Alessandro
Differential Geometry
Metric Geometry
A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an example of a $C^2$ but not $C^3$ length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure.
title Not all sub-Riemannian minimizing geodesics are smooth
topic Differential Geometry
Metric Geometry
url https://arxiv.org/abs/2501.18920