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.
@article{TSG_2015-2016__33__1_0, author = {Valentina Franceschi and Dario Prandi and Luca Rizzi}, title = {Recent results on the essential self-adjointness of {sub-Laplacians,} with some remarks on the presence of characteristic points}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {1--15}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {33}, year = {2015-2016}, doi = {10.5802/tsg.311}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.311/} }
TY - JOUR AU - Valentina Franceschi AU - Dario Prandi AU - Luca Rizzi TI - Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points JO - Séminaire de théorie spectrale et géométrie PY - 2015-2016 SP - 1 EP - 15 VL - 33 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.311/ DO - 10.5802/tsg.311 LA - en ID - TSG_2015-2016__33__1_0 ER -
%0 Journal Article %A Valentina Franceschi %A Dario Prandi %A Luca Rizzi %T Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points %J Séminaire de théorie spectrale et géométrie %D 2015-2016 %P 1-15 %V 33 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.311/ %R 10.5802/tsg.311 %G en %F TSG_2015-2016__33__1_0
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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