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Comptes Rendus. Mathématique

Physique mathématique, Théorie spectrale
Spectre du Laplacien agissant sur les r-tenseurs symétriques sur l’espace hyperbolique
Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 625-630.

Sur l’espace hyperbolique, nous donnons le spectre du Laplacien agissant sur les champs de tenseurs symétriques sans trace de tous rangs.

On the hyperbolic space, we give the spectrum of the Laplacian acting on trace free symmetric tensors fields of any rank.

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DOI : https://doi.org/10.5802/crmath.201
Classification : 35P15,  58J50,  47A53
@article{CRMATH_2021__359_5_625_0,
     author = {Erwann Delay},
     title = {Spectre du {Laplacien} agissant sur les $r$-tenseurs sym\'etriques sur l{\textquoteright}espace hyperbolique},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {625--630},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {5},
     year = {2021},
     doi = {10.5802/crmath.201},
     language = {fr},
}
Erwann Delay. Spectre du Laplacien agissant sur les $r$-tenseurs symétriques sur l’espace hyperbolique. Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 625-630. doi : 10.5802/crmath.201. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.201/

[1] Michael T. Anderson; Piotr T. Chruściel; Erwann Delay Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant. II : (n>4), AdS/CFT correspondence : Einstein metrics and their conformal boundaries (IRMA Lectures in Mathematics and Theoretical Physics), Volume 8, European Mathematical Society, 2005, pp. 165-205 | Zbl 1075.83031

[2] Arthur L. Besse Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 10, Springer, 1987 | MR 867684 | Zbl 0613.53001

[3] Erwann Delay Essential spectrum of the Lichnerowicz Laplacian on symmetric 2-tensors on asymptotically hyperbolic manifolds, J. Geom. Phys., Volume 43 (2002), pp. 33-44 | Article | MR 1911712 | Zbl 1146.58301

[4] Erwann Delay TT-eigentensors for the Lichnerowicz laplacian on some asymptotically hyperbolic manifolds with warped products metrics, Manuscr. Math., Volume 123 (2007) no. 2, pp. 147-165 | Article | MR 2306630 | Zbl 1123.58019

[5] Gregory J. Galloway; Eric Woolgar On static Poincaré–Einstein metrics, J. High Energy Phys., Volume 2015 (2015) no. 6, 51, 18 pages | Zbl 1388.83041

[6] Norihito Koiso Non-deformability of Einstein metrics, Osaka J. Math., Volume 15 (1978), pp. 419-433 | Zbl 0392.53030

[7] John M. Lee Fredholm operators and Einstein metrics on conformally compact manifolds, Memoirs of the American Mathematical Society, 864, American Mathematical Society, 2006 | Zbl 1112.53002

[8] André Lichnerowicz Propagateurs et commutateurs en relativité générale, Publ. Math., Inst. Hautes Étud. Sci., Volume 10 (1961), pp. 5-56 | Article | Numdam

[9] Joseph H. Sampson On a theorem of Chern, Trans. Am. Math. Soc., Volume 177 (1973), pp. 141-153 | Article | MR 317221 | Zbl 0249.53018

[10] Harold C. Steinacker Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models, Adv. Theor. Math. Phys., Volume 25 (2021) no. 4 (to appear)

[11] Yoshihiro Tashiro Complete Riemannian manifolds and some vector fields, Trans. Am. Math. Soc., Volume 117 (1965), pp. 251-275 | Article | MR 174022 | Zbl 0136.17701