Uniqueness results in the inverse spectral Steklov problem

TL;DR

This paper proves that for certain hollow spherical manifolds with warped metrics, the Steklov spectrum uniquely determines the warping function, advancing inverse spectral theory.

Contribution

It establishes a uniqueness result for the inverse Steklov problem on a specific class of warped product manifolds.

Findings

Steklov spectrum determines the warping function uniquely

Results apply to n-dimensional hollow spherical manifolds

Advances inverse spectral problem understanding

Abstract

This paper is devoted to an inverse Steklov problem for a particular class of n-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.