Not all sub-Riemannian minimizing geodesics are smooth
Differential Geometry
2025-02-03 v1 Metric Geometry
Abstract
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 but not length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure.
Cite
@article{arxiv.2501.18920,
title = {Not all sub-Riemannian minimizing geodesics are smooth},
author = {Yacine Chitour and Frédéric Jean and Roberto Monti and Ludovic Rifford and Ludovic Sacchelli and Mario Sigalotti and Alessandro Socionovo},
journal= {arXiv preprint arXiv:2501.18920},
year = {2025}
}