Communications in Mathematical Physics

, Volume 221, Issue 2, pp 255–265

Eigenvalues of the Dirac Operator on Manifolds¶with Boundary

  • Oussama Hijazi
  • Sebastián Montiel
  • Xiao Zhang

DOI: 10.1007/s002200100475

Cite this article as:
Hijazi, O., Montiel, S. & Zhang, X. Commun. Math. Phys. (2001) 221: 255. doi:10.1007/s002200100475


Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized by the existence of real Killing spinors and the minimality of the boundary.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Oussama Hijazi
    • 1
  • Sebastián Montiel
    • 2
  • Xiao Zhang
    • 3
  1. 1.Institut Élie Cartan, Université Henri Poincaré, Nancy I, B.P. 239, 54506 Vandœuvre-Lès-Nancy Cedex, France. E-mail: hijazi@iecn.u-nancy.frFR
  2. 2.Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain.¶E-mail: smontiel@goliat.ugr.esES
  3. 3.Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China. E-mail: