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Séminaire de Théorie spectrale et géométrie (Grenoble)

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Valentina Franceschi; Dario Prandi; Luca Rizzi
Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points
Séminaire de Théorie spectrale et géométrie (Grenoble), 33 (2015-2016), p. 1-15, doi: 10.5802/tsg.311
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Résumé - Abstract

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.

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