67 citations · 132 across the 18 of their papers we have counts for
8 papers · 1 filter
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…
The Sard problem in step 2 and in filiform Carnot groups
Francesco Boarotto, Luca Nalon, Davide Vittone
We study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (de…
A dynamical approach to the Sard problem in Carnot groups
Francesco Boarotto, Davide Vittone
We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajector…
On the codimension of the abnormal set in step two Carnot groups
Alessandro Ottazzi, Davide Vittone
In this article we prove that the codimension of the abnormal set of the endpoint map for certain classes of Carnot groups of step 2 is at least three. Our result applies to all st…
Sard Property for the endpoint map on some Carnot groups
Enrico Le Donne, Richard Montgomery, Alessandro Ottazzi +2
In Carnot-Caratheodory or sub-Riemannian geometry, one of the major open problems is whether the conclusions of Sard's theorem holds for the endpoint map, a canonical map from an i…
Extremal polynomials in stratified groups
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti +1
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterizat…