Spectral estimates on 2-tori

Details Spectral estimates on 2-tori Spectral estimates on 2-tori

2001-01-08

arxiv.org/abs/math/0101061v1

Mathematics

Differential Geometry

uses pstricks package for figures

Scientific paper

We prove upper and lower bounds for the eigenvalues of the Dirac operator and the Laplace operator on 2-dimensional tori. In particluar we give a lower bound for the first eigenvalue of the Dirac operator for non-trivial spin structures. It is the only explicit estimate for eigenvalues of the Dirac operator known so far that uses information about the spin structure. As a corollary we obtain lower bounds for the Willmore functional of a torus embedded into S_3. In the final section we compare Dirac spectra for two different spin structures on an arbitrary Riemannian spin manifold.

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