Not all sub-Riemannian minimizing geodesics are smooth
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912212847689728 |
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| 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 |