Spectral estimates on 2-tori
by
Bernd Ammann


Spectral estimates on 2-tori (.dvi, .ps)
Preprint April 2000

Abstract

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 S3. In the final section we compare Dirac spectra for two different spin structures on an arbitrary Riemannian spin manifold.

Mathematics Subject Classification

53C27 (Primary), 58J50 53C80 (Secondary)

Keywords

Dirac operator, Laplace operator, spectrum, conformal metrics, two-dimensional torus, spin structures, Willmore functional

Bernd Ammann, 2.4.2000