Spectral estimates on 2-tori
by
Bernd Ammann
Spectral estimates on 2-tori
(.dvi,
.ps, .pdf)
Preprint April 2000, available as https://arxiv.org/abs/math/0101061
This preprint will not be published, but a shortened version of this preprint was published under the title
Dirac eigenvalue estimates on 2-tori.
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.
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