These notes aim at illustrating some results achieved in the geometric measure theory in
Carnot groups. They are an extended version of a part of the course Geometric Measure …

The main result of the present article is a Rademacher-type theorem for intrinsic Lipschitz
graphs of codimension in sub-Riemannian Heisenberg groups. For the purpose of proving …

Abstract A Carnot group GG is a connected, simply connected, nilpotent Lie group with
stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as ℂ 1 …

This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular
with the study of the notion of P P-rectifiable measure. First, we show that in arbitrary Carnot …

The purpose of this paper is to introduce and study some basic concepts of quantitative
rectifiability in the first Heisenberg group $\Bbb {H} $. In particular, we aim to demonstrate …

This paper is related to the problem of finding a good notion of rectifiability in sub-
Riemannian geometry. In particular, we study which kind of results can be expected for …

We study singular integral operators induced by 3-dimensional Calderón-Zygmund kernels
in the Heisenberg group. We show that if such an operator is L 2 bounded on vertical …

We provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian
Heisenberg groups in terms of their distributional gradients. Moreover, we prove the …

In this paper, we give a necessary and sufficient condition for a graphical strip in the
Heisenberg group H to be area-minimizing in the slab {-1< x< 1}. We show that our condition …

In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These
graphs are $ C^ 1_H $ regular exactly when the map is uniformly intrinsically differentiable …