Any sub-Riemannian metric has points of smoothness

@article{Agrachev2008AnySM,
  title={Any sub-Riemannian metric has points of smoothness},
  author={A. Agrachev},
  journal={Doklady Mathematics},
  year={2008},
  volume={79},
  pages={45-47}
}
  • A. Agrachev
  • Published 2008
  • Mathematics
  • Doklady Mathematics
We prove the result stated in the title that is equivalent to the existence of a regular point of the sub-Riemannian exponential mapping. In the case of a complete real-analytic sub-Riemannian manifold, we prove that the metric is analytic on an open everywhere dense subset. 
Comparison theorems on H-type sub-Riemannian manifolds
Sub-Riemannian Geodesics
SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS
COMPARISON THEOREMS FOR CONJUGATE POINTS IN SUB-RIEMANNIAN GEOMETRY
Mass Transportation on Sub-Riemannian Manifolds
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