We prove some first order regularity estimates for a class of convex functions in Carnot-Carathéodory spaces, generated by Hörmander vector fields. Our approach relies on both the structure of metric… (More)

We establish an explicit connection between the perimeter measure of an open set E with C1 boundary and the spherical Hausdorff measure SQ−1 restricted to ∂E, when the ambient space is a stratified… (More)

Involutivity is a well known necessary condition for integrability of smooth tangent distributions. We show that this condition is still necessary for integrability with Sobolev surfaces. We… (More)

We prove a coarea inequality for Lipschitz maps between stratified groups. As a consequence we obtain a Sard-type theorem and the nonexistence of nontrivial coarea formulae between Heisenberg groups.… (More)

We review some classical differentiation theorems for measures, showing how they can be turned into an integral representation of a Borel measure with respect to a fixed Carathéodory measure. We… (More)

Let k be a positive integer and letm be the dimension of the horizontal subspace of a stratified group. Under the condition k ≤ m, we show that all submanifolds of codimension k are generically… (More)

We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of… (More)

We show a first nontrivial example of coarea formula for vectorvalued Lipschitz maps defined on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed… (More)

We establish a “low rank property” for Sobolev mappings that pointwise solve a first order nonlinear system of PDEs, whose smooth solutions have the so-called “contact property”. As a consequence,… (More)