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arXiv · 2603.23068

Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds

Tommaso Rossi·Alec Jacopo Almo Schiavoni Piazza·Alessandro Socionovo
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Abstract

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.

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Tommaso Rossi, Alec Jacopo Almo Schiavoni Piazza, Alessandro Socionovo. 2026-03-24. Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds. https://arxiv.org/abs/2603.23068

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