Asma Hassannezhad

Low Steklov eigenvalue of finite area hyperbolic surfaces

The geometry and topology of 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 shortest multi-geodesic cutting the surface into disjoint connected components. In this talk, we discuss a counterpart of Schoen-Wolpert-Yau's inequality for the Steklov eigenvalues on finite area hyperbolic surfaces with geodesic boundary.
This talk is based on joint work with Antoine Métras and Hélène Perrin.