Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914519409754112 |
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| author | Rossi, Tommaso Piazza, Alec Jacopo Almo Schiavoni Socionovo, Alessandro |
| author_facet | Rossi, Tommaso Piazza, Alec Jacopo Almo Schiavoni Socionovo, Alessandro |
| contents | We study the regularity and branching of strictly abnormal minimizing geodesics in sub-Riemannian geometry. We construct examples of real-analytic sub-Riemannian manifolds admitting minimizing geodesics that lose regularity at an interior point of their domain and exhibit branching, thereby resolving longstanding open questions. Moreover, using a lifting procedure, we provide the existence of non-smooth and branching minimizing geodesics also in Carnot groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds Rossi, Tommaso Piazza, Alec Jacopo Almo Schiavoni Socionovo, Alessandro Differential Geometry Metric Geometry We study the regularity and branching of strictly abnormal minimizing geodesics in sub-Riemannian geometry. We construct examples of real-analytic sub-Riemannian manifolds admitting minimizing geodesics that lose regularity at an interior point of their domain and exhibit branching, thereby resolving longstanding open questions. Moreover, using a lifting procedure, we provide the existence of non-smooth and branching minimizing geodesics also in Carnot groups. |
| title | Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2603.23068 |