Rigidity in fixed angle inverse scattering for Riemannian metrics
Abstract
The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally determined inverse problem that is open in general. In this article we consider the rigidity question of distinguishing a sound speed or a Riemannian metric from the Euclidean metric. We prove that a general smooth metric that is Euclidean outside a ball can be distinguished from the Euclidean metric. The methods involve distorted plane waves and a combination of geometric, topological and unique continuation arguments.
Cite
@article{arxiv.2410.06864,
title = {Rigidity in fixed angle inverse scattering for Riemannian metrics},
author = {Lauri Oksanen and Rakesh and Mikko Salo},
journal= {arXiv preprint arXiv:2410.06864},
year = {2025}
}
Comments
Major changes are the following: More details in the proofs of Propositions 2.2, 2.3, 3.1; a correction in the proof of Proposition 2.3; part of the proof of Proposition 3.1 moved to the appendix