Talk by Asma Hassannezhad

The geometry and topology of closed hyperbolic surfaces are subtly reflected in a geometric bound for the Laplace eigenvalues. In 1980, Schoen, Wolpert, and Yau showed that the small Laplace eigenvalues can be bounded from below and above by the length of a collection of closed simple geodesics cutting the surface into disjoint connected components. We discuss this interesting connection for the Steklov eigenvalues on hyperbolic surfaces with geodesic boundaries. These eigenvalues are associated with a first-order elliptic pseudodifferential operator known as the Dirichlet-to-Neumann operator. This talk is based on joint work with Antoine Métras and Hélène Perrin.