779 citations · 2k across the 73 of their papers we have counts for
5 papers · 1 filter
Normal forms and invariants for 2-dimensional almost-Riemannian structures
Ugo Boscain, Grégoire Charlot, Roberta Ghezzi
Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vect…
Anthropomorphic image reconstruction via hypoelliptic diffusion
Ugo Boscain, Jean Duplaix, Jean-Paul Gauthier +1
In this paper we study a model of geometry of vision due to Petitot, Citti and Sarti. One of the main features of this model is that the primary visual cortex V1 lifts an image fro…
On the Hausdorff volume in sub-Riemannian geometry
Andrei Agrachev, Davide Barilari, Ugo Boscain
For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of…
Lipschitz classification of almost-Riemannian distances on compact oriented surfaces
Ugo Boscain, Grégoire Charlot, Roberta Ghezzi +1
Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vect…
Hypoelliptic heat kernel on 3-step nilpotent Lie groups
Ugo Boscain, Jean-Paul Gauthier, Francesco Rossi
In this paper we provide explicitly the connection between the hypoelliptic heat kernel for some 3-step sub-Riemannian manifolds and the quartic oscillator. We study the left-invar…