3 papers
math.FA2026
Characterizations of Sobolev and BV functions on Carnot groups
Francesco Serra Cassano, Kilian Zambanini
We establish two characterizations of real-valued Sobolev and BV functions on Carnot groups. The first is obtained via a nonlocal approximation of the distributional horizontal gra…
math.DG2025
The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group
Sebastiano Nicolussi Golo, Francesco Serra Cassano, Mattia Vedovato
In the first Heisenberg group, we study entire, locally Sobolev intrinsic graphs that are stable for the sub-Riemannian area. We show that, under appropriate integrability conditio…
math.FA2025
On some intrinsic differentiability properties for Absolutely continuous functions between Carnot groups and the Area formula
Andrea Pinamonti, Francesco Serra Cassano, Kilian Zambanini
We discuss Q-absolutely continuous functions between Carnot groups, following Maly's definition for maps of several variables. Such maps enjoy nice regularity properties, like cont…