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

✍ Scribed by Ilka Agricola; Thomas Friedrich

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 734 KB
Volume: 30
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(98)00032-1

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✦ Synopsis

In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface M 2 ~ ~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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