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

Abstract:
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.