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arXiv · 2501.18920

Not all sub-Riemannian minimizing geodesics are smooth

Yacine Chitour·Frédéric Jean·Roberto Monti·Ludovic Rifford·Ludovic Sacchelli·Mario Sigalotti·Alessandro Socionovo
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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 $C^2$ but not $C^3$ length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure.

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Yacine Chitour, Frédéric Jean, Roberto Monti, Ludovic Rifford, Ludovic Sacchelli, Mario Sigalotti, Alessandro Socionovo. 2025-01-31. Not all sub-Riemannian minimizing geodesics are smooth. https://arxiv.org/abs/2501.18920

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