Curvature and comparison theorems for the sub-Laplacians

Jeudi 31 mai 2018 14:00-15:00 - Erlend Grong - Orsay

Résumé : We study hypoelliptic second order differential operators that are not elliptic, but satisfy the strong Hörmander condition. Just as elliptic operators correspond to a Riemannian geometric structure, such hypoelliptic operators correspond to a sub-Riemannian geometric structure. One can consider sub-Riemannian manifolds as the limit of Riemannian manifolds where the length of vectors in a certain subbundle go to infinity. Unfortunately, this limit will make the Ricci curvature become unbounded. Hence, we loose important results in the process, such as the Laplace comparison theorem.
We will show how to recover a comparison theorem for certain cases. We will consider sub-Riemannian manifolds that appear as limits of totally geodesic foliations. In particular, we will focus on Sasakian manifolds. The results we obtain allows us to determine global properties of our manifold, such as compactness and diameter bound, from just partial properties of its curvature.
This result is a joint work with Fabrice Baudoin, Kazumasa Kuwada and Anton Thalmaier.

Lieu : salle 2L8 (IMO, bat. 307)

Notes de dernières minutes : Café culturel assuré à 13h par Patrick Massot.

Curvature and comparison theorems for the sub-Laplacians  Version PDF