1 citations · 1 across the 7 of their papers we have counts for
8 papers
A BMO-type representation formula for the total variation of SBV functions in Heisenberg groups
Marco Di Marco, Sebastiano Don, Davide Vittone
We prove a formula for the total variation of SBV functions in sub-Riemannian Heisenberg groups arising as the limit of certain BMO-type functionals.
Quantization of measures in Carnot groups
Marco Di Marco, Mikaela Iacobelli
We study optimal quantization of probability measures on Carnot groups equipped with a left-invariant homogeneous distance. We prove two main results. First, we establish a Zador-t…
Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces
Marco Di Marco
By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincaré inequality for special functions with bounded v…
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…
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…
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 res…
Stepanov Differentiability Theorem for intrinsic graphs in Heisenberg groups
Marco Di Marco, Andrea Pinamonti, Davide Vittone +1
We prove a Stepanov differentiability type theorem for intrinsic graphs in sub-Riemannian Heisenberg groups.
Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
Marco Di Marco, Antoine Julia, Sebastiano Nicolussi Golo +1
We introduce and study the notion of -regular submanifold with boundary in sub-Riemannian Heisenberg groups. As an application, we prove a version of Stokes' Theore…