Event

Talk
Small Eigenvalues and analytic systole of surfaces
Werner Ballmann (Bonn)
9 Dec 2016, 10:00 – 11:00

Eigenvalues of a Riemannian manifolds M are called small if they lie below the bottom of the spectrum of the universal covering of M . For example, eigenvalues of hyperbolic surfaces below a quarter are small. I will explain some of the results of Buser and others on small eigenvalues of hyperbolic surfaces. In my recent joint work with Matthiesen and Mondal on small eigenvalues of Riemannian
surfaces, a new invariant, the analytic systole Λ of S, arises naturally. I will
discuss Λ and its relation to small eigenvalues of S.