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  • Séminaire de théorie spectrale et géométrie
  • Volume 33 (2015-2016)
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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.
  • 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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Published online: 2018-08-27
DOI: 10.5802/tsg.311
Author's affiliations:
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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@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/}
}
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SP  - 1
EP  - 15
VL  - 33
PB  - Institut Fourier
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%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
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%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/
  • References
  • Cited by

[1] Andrei Agrachev; Ugo Boscain; Jean-Paul Gauthier; Francesco Rossi The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups, J. Funct. Anal., Volume 256 (2009) no. 8, pp. 2621-2655 http://www.sciencedirect.com/science/article/pii/s0022123609000202 | DOI | Zbl

[2] Davide Barilari; Luca Rizzi A formula for Popp’s volume in sub-Riemannian geometry, Anal. Geom. Metr. Spaces, Volume 1 (2013), pp. 42-57 | DOI | MR | Zbl

[3] Ugo Boscain; Camille Laurent The Laplace-Beltrami operator in almost-Riemannian geometry, Ann. Inst. Fourier, Volume 63 (2013) no. 5, pp. 1739-1770 | DOI | MR | Zbl

[4] Valentina Franceschi; Dario Prandi; Luca Rizzi On the essential self-adjointness of sub-Laplacians (2017) (https://arxiv.org/abs/1708.09626)

[5] Roberta Ghezzi; Frédéric Jean On measures in sub-Riemannian geometry, Sémin. Théor. Spectr. Géom., Volume 33 (2018), p. xxx-xxx

[6] Richard Montgomery A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, 91, American Mathematical Society, 2002, xx+259 pages | MR | Zbl

[7] Gheorghe Nenciu; Irina Nenciu On confining potentials and essential self-adjointness for Schrödinger operators on bounded domains in ℝ n , Ann. Henri Poincaré, Volume 10 (2009) no. 2, pp. 377-394 | DOI | MR | Zbl

[8] Dario Prandi; Luca Rizzi; Marcello Seri Quantum confinement on non-complete Riemannian manifolds (2017) (https://arxiv.org/abs/1609.01724, to appear in J. Spectr. Theory)

[9] Michael Reed; Barry Simon Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press, 1975, xv+361 pages | MR | Zbl

[10] Robert S. Strichartz Sub-Riemannian geometry, J. Differ. Geom., Volume 24 (1986) no. 2, pp. 221-263 http://projecteuclid.org/euclid.jdg/1214440436 | MR | Zbl

[11] Robert S. Strichartz Corrections to: “Sub-Riemannian geometry”, J. Differ. Geom., Volume 30 (1989) no. 2, pp. 595-596 http://projecteuclid.org/euclid.jdg/1214443604 | MR

[12] Yves Colin de Verdière; Françoise Truc Confining quantum particles with a purely magnetic field, Ann. Inst. Fourier, Volume 60 (2010) no. 7, pp. 2333-2356 http://aif.cedram.org/item?id=aif_2010__60_7_2333_0 | MR | Zbl

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