6 papers
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…
On low-dimensional uniform rectifiability in Heisenberg groups
Katrin Fässler, Andrea Pinamonti, Kilian Zambanini
Refining an earlier result due to Hahlomaa, we provide a new Carleson-type condition for -regular sets in the Heisenberg group to have big pieces of Lipschitz ima…
Minimal Banach-Tarski decompositions
Cesare Straffelini, Kilian Zambanini
We investigate the problem of finding the minimum number of pieces necessary for dividing a three-dimensional sphere or a ball and reassembling it to form congruent copies of t…
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.
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…
Maz'ya-Shaposhnikova meet Bishop-Gromov
Bang-Xian Han, Andrea Pinamonti, Zhefeng Xu +1
We find a surprising link between Maz'ya-Shaposhnikova's well-known asymptotic formula concerning fractional Sobolev seminorms and the generalized Bishop-Gromov inequality. In the…