Fill-ins, Dirac eigenvalues and the hyperspherical radius

27.06.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Christian Bär (UP)

Let \(M\) be an n-dimensional closed Riemannian spin manifold. A fill-in of \(M\) is a compact (n+1)-dimensional Riemannian spin manifold \(X\) whose boundary is \(M\). If \(X\) has nonnegative scalar curvature, we will call it an NNSC fill-in. As predicted by Gromov, the boundary mean curvature on NNSC fill-ins of \(M\) cannot become arbitrarily large. I will explain how the mean curvature can be bounded by intrinsic Dirac eigenvalues of \(M\) and how this implies a bound in terms of the hyperspherical radius of \(M\).