4 papers
A note on the diameter of small sub-Riemannian balls
Marco Di Marco, Gianluca Somma, Davide Vittone
We observe that the diameter of small (in a locally uniform sense) balls in sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of t…
Renormalization of contact vector fields with horizontal Sobolev regularity in Heisenberg groups
Luigi Ambrosio, Gianluca Somma, Simone Verzellesi +1
In this paper we obtain the well-posedness of the transport and continuity equations in the Heisenberg groups for a class of contact vector fields , under…
SBV functions in Carnot-Carathéodory spaces
Marco Di Marco, Sebastiano Don, Davide Vittone
We introduce the space SBV of special functions with bounded -variation in Carnot-Carathéodory spaces and study its main properties. Our main outcome is an approximation re…
Submanifolds with boundary in sub-Riemannian Heisenberg Groups
Marco Di Marco, Davide Vittone
We discuss the notion of submanifolds with boundary with intrinsic regularity in sub-Riemannian Heisenberg groups and we provide some examples. Eventually, we present a Stoke…