20 citations · 31 across the 8 of their papers we have counts for
14 papers
Monotone sets and local minimizers for the perimeter in Carnot groups
Séverine Rigot
Monotone sets have been introduced about ten years ago by Cheeger and Kleiner who reduced the proof of the non biLipschitz embeddability of the Heisenberg group into to the c…
Precisely monotone sets in step-2 rank-3 Carnot algebras
Daniele Morbidelli, Séverine Rigot
A subset of a Carnot group is said to be precisely monotone if the restriction of its characteristic function to each integral curve of every left-invariant horizontal vector field…
Horizontally affine functions on step-2 Carnot algebras
Enrico Le Donne, Daniele Morbidelli, Séverine Rigot
In this paper we introduce the notion of horizontally affine, h-affine in short, function and give a complete description of such functions on step-2 Carnot algebras. We show that…
Quantitative notions of rectifiability in the Heisenberg groups
Séverine Rigot
Several quantitative notions of rectifiability in the Heisenberg groups have emerged in the recent literature. In this paper we study the relationship between two of them, the big…
Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group
Katrin Fässler, Tuomas Orponen, Séverine Rigot
A Semmes surface in the Heisenberg group is a closed set that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. E…
The Besicovitch covering property in the Heisenberg group revisited
Sebastiano Golo, Séverine Rigot
The Besicovitch covering property (BCP) is known to be one of the fundamental tools in measure theory, and more generally, a usefull property for numerous purposes in analysis and…