Group Analysis of Differential Equations and Integrable Systems − 2018
(National and Kapodistrian University of Athens, Greece)
Riemannian metrics and Laplacians for generalised smooth distributions
Generalised smooth distributions arise in several contexts, in particular
they include all singular foliations and all the distributions arising in
sub-Riemannian Geometry. We construct a Riemannian metric for any
distribution as such and use it to define a geometric Laplace operator.
Using the longitudinal pseudodifferential calculus of the smallest
foliation including the distribution, we show that this Laplacian is
self-adjoint and hypoelliptic.
This is joint work with Yuri Kordyukov.