Closure of the Laplace-Beltrami Operator on 2D Almost-Riemannian Manifolds and Semi-Fredholm Properties of Differential Operators on Lie Manifolds

Abstract The problem of determining the domain closure Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory Lie groupoids natural domains perturbations are found. main novelty that presented method allows us to treat geometries with tangency points. This kind singularity difficult since those points do not have tubular neighbourhood compatible metric.