Branching of regular abnormal geodesics in sub-Riemannian manifolds of rank two

2026/07/31 by Luca Rizzi, Mario Sigalotti, Nicolò Tedesco
Mathematics · #math.DG #msc:53C17 #msc:49J15

paper · pdf

32 pages, 5 figures

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

We study branching of regular abnormal geodesics in sub-Riemannian manifolds of rank two. As an application, we provide examples of two new phenomena: continuous families of strictly abnormal branching geodesics, and geodesics with an accumulation of countably many branching points.

Citations

• Normal Curves in Sub-Finsler Lie Groups: Branching for Strongly Convex Norms and Face Stability for Polyhedral Norms
• On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures
• Existence and uniqueness of optimal transport maps
• Shortest paths for sub-Riemannian metrics on rank-two distributions