Path isometric embedding of sub-Riemannian manifolds (I)

In 1954, John Nash showed that any Riemannian manifold can be path isometrically embedded into some Euclidean space. In this talk, I will prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curve in the manifold. This result is due to Enrico Le Denne and it is an extension of Nash's embedding theorem.