Group Analysis of Differential Equations and Integrable Systems − 2018

Iakovos Androulidakis (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.