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.

21 pages, 1 figure

References in corpus (4)

• A formula for Popp's volume in sub-Riemannian geometry
• Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry
• Quantum confinement on non-complete Riemannian manifolds
• Tubular neighborhoods in the sub-Riemannian Heisenberg groups

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