Work

Rigidity for Fixed Angle Inverse Scattering for Riemannian Metrics

Year: 2026

Type: article

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.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1702623

Authors: Lauri Oksanen, Rakesh, Mikko Salo

Institutions: University of Helsinki, University of Delaware, University of Jyväskylä

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Academy of Finland, H2020 European Research Council