Inserted: 15 mar 2019
Last Updated: 15 mar 2019
Journal: Séminaire de Théorie spectrale et géométrie (Grenoble)
In this proceeding, we present some recent results obtained in 4 on the essential self-adjointness of sub-Laplacians on non-complete sub-Riemannian manifolds. A notable application is the proof of the essential self-adjointness of the Popp sub-Laplacian on the equiregular connected components of a sub-Riemannian manifold, when the singular region does not contain characteristic points. In their presence, the self-adjointness properties of (sub-)Laplacians are still unknown. We conclude the paper discussing the difficulties arising in this case.