Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 330

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

I. Agricola and T. Friedrich

In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface M2 -> R3 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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