5 citations · 12 across the 12 of their papers we have counts for
8 papers · 1 filter
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…
Higher order Goh conditions for singular extremals of corank 1
Francesco Boarotto, Roberto Monti, Alessandro Socionovo
We prove Goh conditions of order n for strictly singular length minimizing curves of corank 1, under the assumption that the lower order intrinsic differentials of the end-point ma…
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…
Third order open mapping theorems and applications to the end-point map
Francesco Boarotto, Roberto Monti, Francesco Palmurella
This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a fi…
Structure of the endpoint map near nice singular curves
Andrei A. Agrachev, Francesco Boarotto
Given a rank-two sub-Riemannian structure and a point , a singular curve is a critical point of the endpoint map defined on the space of horizont…
Homotopically Invisible Singular Curves
Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario
Given a smooth manifold and a totally nonholonomic distribution of rank , we study the effect of singular curves on the topology of the space of horizontal pat…
Homotopy properties of endpoint maps and a theorem of Serre in subriemannian geometry
Francesco Boarotto, Antonio Lerario
We discuss homotopy properties of endpoint maps for affine control systems. We prove that these maps are Hurewicz fibrations with respect to some topology on the space of…
Conformal equivalence of sub-Riemannian 3D contact structures on Lie groups
Francesco Boarotto
In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy:…