Uniqueness and stability for an inverse Steklov problem

(22 mars 2021 / March 22, 2021) Young researchers in spectral geometry II (Mini-conférence)

Germain Gendron (Université de Nantes, France)
Uniqueness and stability for an inverse Steklov problem

Abstract:
In this talk, we present results for an inverse Steklov problem for a particular class of 2-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. We prove that the knowledge of the Steklov spectrum determines uniquely the associated warping function up to a natural invariance. Then, we study the continuous dependence of the warping function defining the warped product with respect to the Steklov spectrum.