Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points
Valentina Franceschi1; Dario Prandi2; Luca Rizzi3
1 Inria, team GECO & LJLL Université Pierre et Marie Curie Paris (France)
2 CNRS, Laboratoire des Signaux & Systémes, CentraleSupélec Gif-sur-Yvette (France)
3 Univ. Grenoble Alpes, CNRS, Institut Fourier 38000 Grenoble (France)
Séminaire de théorie spectrale et géométrie, Volume 33 (2015-2016), pp. 1-15.

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.

Published online:
DOI: 10.5802/tsg.311
Valentina Franceschi 1; Dario Prandi 2; Luca Rizzi 3

1 Inria, team GECO & LJLL Université Pierre et Marie Curie Paris (France)
2 CNRS, Laboratoire des Signaux & Systémes, CentraleSupélec Gif-sur-Yvette (France)
3 Univ. Grenoble Alpes, CNRS, Institut Fourier 38000 Grenoble (France) 
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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, Volume 33 (2015-2016), pp. 1-15. doi : 10.5802/tsg.311. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.311/

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