Communications in Mathematical Physics

, Volume 221, Issue 2, pp 255–265

Eigenvalues of the Dirac Operator on Manifolds¶with Boundary


  • Oussama Hijazi
    • Institut Élie Cartan, Université Henri Poincaré, Nancy I, B.P. 239, 54506 Vandœuvre-Lès-Nancy Cedex, France. E-mail:
  • Sebastián Montiel
    • Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain.¶E-mail:
  • Xiao Zhang
    • Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China. E-mail:

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.

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© Springer-Verlag Berlin Heidelberg 2001