Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds
Differential Geometry
2026-05-01 v3 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2603.23068,
title = {Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds},
author = {Tommaso Rossi and Alec Jacopo Almo Schiavoni Piazza and Alessandro Socionovo},
journal= {arXiv preprint arXiv:2603.23068},
year = {2026}
}