Not all sub-Riemannian minimizing geodesics are smooth
arXiv:2501.18920
Abstract
A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an example of a but not length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure.