The sub-Riemannian Sard conjecture asks whether the endpoints of all abnormal curves from a fixed point have measure
zero. Restricting to abnormal curves that minimize length
gives a different assertion.
Agrachev, A.; Barilari, D.; and Boscain, U. A Comprehensive Introduction to Sub-Riemannian Geometry: From the Hamiltonian Viewpoint. Cambridge,
England: Cambridge University Press, 2019. https://doi.org/10.1017/9781108677325.Wang,
B. and Zelenko, I. "An Equiregular Counterexample to the Sard Conjecture for
Sub-Riemannian Endpoint Maps." 16 Oct 2026. https://arxiv.org/abs/2610.24080.
