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

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

1998-06-15

arxiv.org/abs/math/9806081v1

Mathematics

Differential Geometry

Latex2.09, 23 pages

Scientific paper

10.1016/S0393-0440(98)00032-1

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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