Laplace eigenvalues and minimal surfaces in spheres.
Spectrum of the Laplace-Beltrami operator is one of the fundamental invariants of a Riemannian manifold. It has many applications, perhaps the most significant is in connection to minimal surfaces. In this talk we will show how minimal surfaces arise in the study of optimal upper bounds for Laplace eigenvalues. We will give an overview of recent results in this area, including the sharp upper bound for all eigenvalues on the two-dimensional sphere obtained jointly with N. Nadirashvili, A. Penskoi and I. Polterovich.
Refreshments in Math Commons Room at 3:30pm