preprint

Inserted: 1 may 2026

Year: 2026

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.