Title: On the essential self-adjointness of singular sub-Laplacians,
Abstract: We prove a general essential self-adjointness criterion for sub-Laplacians on
complete sub-Riemannian manifolds, defined with respect to singular measures.
As a consequence, we show that the intrinsic sub-Laplacian (i.e. defined w.r.t.
Popp's measure) is essentially self-adjoint on the equiregular connected
components of a sub-Riemannian manifold. This result holds under mild
regularity assumptions on the singular region, and when the latter does not
contain characteristic points.