Lower bounds for the eigenvalues of the Spin<sup><i>c</i></sup> Dirac operator on manifolds with boundary

Roger Nakad; Julien Roth

doi:10.1016/j.crma.2015.12.017

Differential geometry

Lower bounds for the eigenvalues of the Spin^c Dirac operator on manifolds with boundary

Presented by: the Editorial Board

Roger Nakad ¹; Julien Roth ²

¹ Notre Dame University-Louaize, Faculty of Natural and Applied Sciences, Department of Mathematics and Statistics, P. O. Box 72, Zouk Mikael, Lebanon
² LAMA, Université Paris-Est Marne-la-Vallée, Cité Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 425-431.

Abstract
Résumé

We extend the Friedrich inequality for the eigenvalues of the Dirac operator on ${Spin}^{c}$ manifolds with boundary under different boundary conditions. The limiting case is then studied and examples are given.

Nous étendons l'inégalité de Friedrich pour les valeurs propres de l'opérateur de Dirac sur les variétés ${Spin}^{c}$ à bord pour différentes conditions à bord. Le cas limite est étudié et des exemples sont donnés.

Received: 2014-10-30
Accepted: 2015-12-16
Published online: 2016-02-11

DOI: 10.1016/j.crma.2015.12.017

Author's affiliations:

Roger Nakad ¹; Julien Roth ²

¹ Notre Dame University-Louaize, Faculty of Natural and Applied Sciences, Department of Mathematics and Statistics, P. O. Box 72, Zouk Mikael, Lebanon
² LAMA, Université Paris-Est Marne-la-Vallée, Cité Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France

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     author = {Roger Nakad and Julien Roth},
     title = {Lower bounds for the eigenvalues of the {Spin\protect\textsuperscript{\protect\emph{c}}} {Dirac} operator on manifolds with boundary},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {425--431},
     publisher = {Elsevier},
     volume = {354},
     number = {4},
     year = {2016},
     doi = {10.1016/j.crma.2015.12.017},
     language = {en},
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Roger Nakad; Julien Roth. Lower bounds for the eigenvalues of the Spin^c Dirac operator on manifolds with boundary. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 425-431. doi : 10.1016/j.crma.2015.12.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.017/

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