Differential geometry
On an inequality of Brendle in the hyperbolic space
Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 322-326.

We give a spinorial proof of a Heintze–Karcher-type inequality in the hyperbolic space proved by Brendle [4]. The proof relies on a generalized Reilly formula on spinors recently obtained in [7].

On donne une nouvelle démonstration d'une inégalité de type Heintze–Karcher dans l'espace hyperbolique prouvée par Brendle [4]. Cette preuve repose sur une formule de Reilly généralisée pour l'opérateur de Dirac, que nous avons récemment obtenue dans [7].

Received:
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Published online:
DOI: 10.1016/j.crma.2018.01.015
Hijazi, Oussama 1; Montiel, Sebastián 2; Raulot, Simon 3

1 Institut Élie-Cartan, Université de Lorraine, Nancy, B.P. 239, 54506 Vandœuvre-Lès-Nancy cedex, France
2 Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
3 Laboratoire de mathématiques Raphaël-Salem, UMR 6085 CNRS – Université de Rouen, avenue de l'Université, B.P. 12, Technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France
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Hijazi, Oussama; Montiel, Sebastián; Raulot, Simon. On an inequality of Brendle in the hyperbolic space. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 322-326. doi : 10.1016/j.crma.2018.01.015. http://www.numdam.org/articles/10.1016/j.crma.2018.01.015/

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