Dirac eigenvalue estimates on surfaces

Details Dirac eigenvalue estimates on surfaces Dirac eigenvalue estimates on surfaces

2002-01-25

arxiv.org/abs/math/0201249v1

Math. Zeitschr. 240 , 423-449 (2002)

Mathematics

Differential Geometry

to appear in Math. Zeitschrift

Scientific paper

We prove lower Dirac eigenvalue bounds for closed surfaces with a spin structure whose Arf invariant equals 1. Besides the area only one geometric quantity enters in these estimates, the spin-cut-diameter which depends on the choice of spin structure. It can be expressed in terms of various distances on the surfaces or, alternatively, by stable norms of certain cohomology classes. In case of the 2-torus we obtain a positive lower bound for all Riemannian metrics and all nontrivial spin structures. The corresponding estimate also holds for the $L^2$-spectrum of the Dirac operator on a noncompact complete surface of finite area. As a corollary we get positive lower bounds on the Willmore integral for all 2-tori embedded in $R^3$.

Affiliated with

Also associated with

No associations

Rating

Dirac eigenvalue estimates on surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dirac eigenvalue estimates on surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac eigenvalue estimates on surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-362261