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Upper bounds for the first eigenvalue of the Dirac operator on surfaces

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Publication Date
Volume
30
Issue
1
Identifiers
DOI: 10.1016/s0393-0440(98)00032-1
Keywords
  • Differential Geometry
  • Dirac Operator
  • Spectrum
  • Surfaces

Abstract

Abstract In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface M 2 ↪ R 3 as well as intrinsic bounds for two-dimensional compact manifolds of genus zero and genus one. Moreover, we compare the different estimates of the eigenvalue of the Dirac operator for special families of metrics.

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