Large Steklov Eigenvalues Under Geometric Constraints

Explore a seminar talk on spectral geometry focusing on large Steklov eigenvalues under geometric constraints. Delve into recent constructions of compact Riemannian manifolds with boundary that satisfy specific geometric conditions and exhibit arbitrarily large first non-zero Steklov eigenvalues. Examine two key aspects: first, the creation of Riemannian metrics on given manifolds with fixed boundary metrics and volumes, showcasing the first examples in three-dimensional manifolds; second, investigate the construction of compact submanifolds in Euclidean space with fixed boundaries and arbitrarily large first non-zero Steklov eigenvalues. Gain insights into this collaborative research presented by Panagiotis Polymerakis from the University of Thessaly, part of the Spectral Geometry in the Clouds seminar series.