On the first eigenvalue on degenerating hyperbolic surfaces
speaker: Nadine Grosse (University of Freiburg)abstract: We consider the first non-zero eigenvalue $\lambda1$ of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that $8\pi \nabla \log \lambda1$ essentially agrees with the dual of the differential of the degenerating Fenchel-Nielson length coordinate. This result is mainly based on analysing properties of holomorphic quadratic differentials and relating quadratic holomorphic differentials to Fenchel-Nielson coordinates. As a corollary we obtain that $\lambda1$ essentially only depends on the length of the collapsing geodesic $\sigma$ and the topology of $M \setminus \sigma$, with error estimates that are sharp for all surfaces of genus greater than 2. This is joint work with Melanie Rupflin (Oxford), arXiv: 1701.08491.
timetable:
Tue 5 Jun, 10:20 - 11:20, Aula Dini
<< Go back