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

Ilka Agricola·Thomas Friedrich
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Abstract

In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface $M^2 \hookrightarrow {\Bbb R}^3$ as well as intrinsic bounds for 2-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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Ilka Agricola, Thomas Friedrich. 1998-06-15. Upper bounds for the first eigenvalue of the Dirac operator on surfaces. https://doi.org/10.1016/s0393-0440(98)00032-1

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