4 citations · 4 across the 2 of their papers we have counts for
4 papers
Area of intrinsic graphs and coarea formula in Carnot Groups
Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone
We consider submanifolds of sub-Riemannian Carnot groups with intrinsic regularity (). Our first main result is an area formula for intrinsic graphs; as an app…
Uniform energy distribution in a pattern-forming system of surface charges
Katarina Bellova, Antoine Julia, Felix Otto
We consider a variational model for a charge density on a (hyper)plane, with a short-range attraction coming from the interfacial energy and a long-range repulsion c…
Intrinsic rectifiability via flat cones in the Heisenberg group
Antoine Julia, Sebastiano Nicolussi Golo
We give a geometric criterion for a topological surface in the first Heisenberg group to be an intrinsic Lipschitz graph, using planar cones instead of the usual open cones.
A Henstock-Kurzweil type integral on 1 dimensional integral currents
Antoine Julia
We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Inte…