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Lower Bounds for the Eigenvalues of the Dirac Operator: Part I. The Hypersurface Dirac Operator

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Abstract

We give optimal lower bounds for the hypersurface Diracoperator in terms of the Yamabe number, the energy-momentum tensor andthe mean curvature. In the limiting case, we prove that the hypersurfaceis an Einstein manifold with constant mean curvature.

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Authors and Affiliations

  1. Institut Élie Cartan, Université Henri Poincaré, Nancy 1, B.P. 239, 54506, Vandoeuvre-Lès-Nancy Cedex, France

    Oussama Hijazi

  2. Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Xiao Zhang

Authors
  1. Oussama Hijazi
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  2. Xiao Zhang
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Hijazi, O., Zhang, X. Lower Bounds for the Eigenvalues of the Dirac Operator: Part I. The Hypersurface Dirac Operator. Annals of Global Analysis and Geometry 19, 355–376 (2001). https://doi.org/10.1023/A:1010749808691

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