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#### Mathematisches Kolloquium

„Small eigenvalues of the Laplacian on surfaces“
Prof. Dr. Werner Ballmann, MPI Bonn und Uni Bonn

Eigenvalues of the Laplacian on hyperbolic surfaces are called small, if they lie below $1/4$, the bottom of the spectrum of the Laplacian on the hyperbolic plane. Buser showed that, for any $\varepsilon>0$, the closed surface $S$ of genus $g\ge2$ carries a hyperbolic metric such that $\lambda_{2g−3}<\varepsilon$, where $\lambda_0 = 0 < \lambda_1 \le \lambda_2 \le \ldots$ denotes the sequence of eigenvalues of the Laplacian of the metric on $S$. He also showed that $\lambda_{2g−2}\ge c>0$, where c is independent of genus and hyperbolic metric. Buser's results were extended and refined by Schmutz, and he and Schmutz conjectured that $\lambda_{2g−2}\ge1/4$ for any hyperbolic metric on $S$. I will discuss this conjecture, its solution by Otal and Rosas, and recent progress. (Joint work with Henrik Matthiesen and Sugata Mondal.)

Donnerstag, den 28. Mai 2015 um 17 Uhr c.t. Uhr, in INF 288, HS2 Donnerstag, den 28. Mai 2015 at 17 Uhr c.t., in INF 288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. A. Wienhard