Large Steklov eigenvalues under geometric constraints
Analysis and Geometry Seminar
22nd February 2024, 3:30 pm – 4:30 pm
Fry Building, 2.04
In this talk, we will discuss two recent constructions of compact Riemannian manifolds with boundary which satisfy certain geometric conditions and have arbitrarily large first non-zero Steklov eigenvalue. In the first part of the talk, under some assumptions, we will construct Riemannian metrics on a given manifold which coincide on the boundary, have fixed volume and arbitrarily large first non-zero Steklov eigenvalue. In particular, this provides the first examples of Riemannian metrics with these properties on three-dimensional manifolds. In the second part, we will construct compact submanifolds of the Euclidean space with fixed boundary which have arbitrarily large first non-zero Steklov eigenvalue.