4 citations · 6 across the 7 of their papers we have counts for
11 papers
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…
Cantor sets with absolutely continuous harmonic measure
Guy David, Cole Jeznach, Antoine Julia
We construct Ahlfors regular Cantor sets of small dimension in the plane, such that the Hausdorff measure on is equivalent to the harmonic measure associated to its complem…
Flat compactness of normal currents, and charges in Carnot groups
Antoine Julia, Pierre Pansu
We prove that the family of normal currents in the sense of Rumin in a Carnot group is compact in the flat topology. This result is obtained through a dual compactness argument for…
On sets with unit Hausdorff density in homogeneous groups
Antoine Julia, Andrea Merlo
It is a longstanding conjecture that given a subset of a metric space, if has finite Hausdorff measure in dimension and has unit density…
Lipschitz functions on submanifolds in Heisenberg groups
Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone
We study the behavior of Lipschitz functions on intrinsic submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We…
Nowhere differentiable intrinsic Lipschitz graphs
Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone
We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneou…