Asma Hassannezhad

Geometric lower bounds for Steklov eigenvalues

In 1970, Cheeger obtained a beautiful geometric lower bound for the first nonzero eigenvalue of the Laplacian in term of an isoperimetric constant. The generalization of the Cheeger inequality to higher order eigenvalues of the Laplacian in discrete and manifold settings has been studied in recent years. In this talk, I introduce the Steklov eigenvalue problem and its connection with the Laplace eigenvalues. Then we study the Cheeger type inequalities for the Steklov eigenvalues which give interesting geometric lower bounds for the k-th Steklov eigenvalue. This is joint work with Laurent Miclo.