Riemannian metrics and Laplacians for smooth generalised distributions
Citation:
Androulidakis I, Kordyukov Y. Riemannian metrics and Laplacians for smooth generalised distributions. Journal of Topology and Analysis [Internet]. 2021;13(2):395-442.
We show that any generalised smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying manifold is compact, we show that it is essentially self-adjoint. Viewing this Laplacian in the longitudinal pseudodifferential calculus of the smallest singular foliation which includes the distribution, we prove hypoellipticity.
National and Kapodistrian University of Athens, Department of Mathematics (+30) 210-7276423 Panepistimiopolis Zografou Athens, ZipCode 157-84 iandroul@math.uoa.gr
