Eigenvalue Boundary Problems for the Dirac Operator |
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Authors: | Oussama Hijazi Sebastián Montiel Antonio Roldán |
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Institution: | (1) Institut élie Cartan, Université Henri Poincaré, Nancy I, B.P. 239, 54506 Vandoe uvre-Lès-Nancy Cedex, France. E-mail: hijazi@iecn.u-nancy.fr, FR;(2) Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain. E-mail: smontiel@goliat.ugr.es; aroldan@goliat.ugr.es, ES |
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Abstract: | On a compact Riemannian spin manifold with mean-convex boundary, we analyse the ellipticity and the symmetry of four boundary
conditions for the fundamental Dirac operator including the (global) APS condition and a Riemannian version of the (local)
MIT bag condition. We show that Friedrich's inequality for the eigenvalues of the Dirac operator on closed spin manifolds
holds for the corresponding four eigenvalue boundary problems. More precisely, we prove that, for both the APS and the MIT
conditions, the equality cannot be achieved, and for the other two conditions, the equality characterizes respectively half-spheres
and domains bounded by minimal hypersurfaces in manifolds carrying non-trivial real Killing spinors.
Received: 12 November 2001 / Accepted: 25 June 2002 Published online: 21 October 2002
RID="*"
ID="*" Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967 and by European Union FEDER
funds |
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