63 citations · 200 across the 19 of their papers we have counts for
3 papers · 1 filter
Hypoelliptic diffusion and human vision: a semi-discrete new twist
Ugo Boscain, Roman Chertovskih, Jean-Paul Gauthier +1
This paper presents a semi-discrete alternative to the theory of neurogeometry of vision, due to Citti, Petitot and Sarti. We propose a new ingredient, namely working on the group…
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…
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
Andrei Agrachev, Ugo Boscain, Jean-Paul Gauthier +1
We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp's volume form introduced by Montgomery. Th…