Enrico Le Donne

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We prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curves in the manifold. The result is an extension of Nash C Embedding Theorem. For more general metric spaces the same result is false, e.g., for Finsler non-Riemannian manifolds. However, we also show that any metric space of finite(More)
We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G then, for almost every x ∈ G with respect to the perimeter measure of E, some tangent of E at x is a vertical halfspace. This is a partial extension of a theorem of Franchi-Serapioni-Serra Cassano in step 2 Carnot groups:(More)
In Carnot-Carathéodory or sub-Riemannian geometry, one of the major open problems is whether the conclusions of Sard’s theorem holds for the endpoint map, a canonical map from an infinite-dimensional path space to the underlying finite-dimensional manifold. The set of critical values for the endpoint map is also known as abnormal set, being the set of(More)