# American Institute of Mathematical Sciences

August  2020, 14(4): 631-664. doi: 10.3934/ipi.2020029

## Uniqueness results in the inverse spectral Steklov problem

 Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, 2 Rue de la Houssinière BP 92208, F-44322 Nantes Cedex 03, France

Received  June 2019 Revised  January 2020 Published  May 2020

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.

Citation: Germain Gendron. Uniqueness results in the inverse spectral Steklov problem. Inverse Problems & Imaging, 2020, 14 (4) : 631-664. doi: 10.3934/ipi.2020029
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