Séance Séminaire

Séminaire Gaston Darboux

The volume and the Laplacian in Riemannian and sub-Riemannian geometry

In this talk, I will discuss the problem of defining in sub-Riemannian geometry an hypoelliptic operator generalizing the Laplace-Beltrami operator. This problem is strictly related to the problem of defining intrinsically a volume in sub-Riemannian geometry. Indeed starting from dimension 5, the Popp volume (that is a possible generalization of the Riemannian volume) does not cincide anymore with the spherical Hausdorff volume. The random-walk point of view provides some interesting information.