25.07.2024, 16:30
– Raum 0.14
Forschungsseminar Differentialgeometrie
Dirac eigenvalues, hyperspherical radius and applications
Christian Bär (UP)
It has recently been conjectured that the eigenvalues λ of the Dirac operator on a closed Riemannian spin manifold M of dimension n ≥ 3 can be estimated from below by the total scalar curvature:
<tex>\lambda^2\geq\frac{n}{4(n-1)}\cdot\frac{\int_{M} S}{vol(M)}</tex>
We show by example that such an estimate is impossible.