Rigidity for Fixed Angle Inverse Scattering for Riemannian Metrics
Abstract
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.
Fields of Study & Subjects
Numerical methods in inverse problems
Microwave Imaging and Scattering Analysis
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 1
- Pages
- 308–334
- Publication date
- 13 January 2026
- Language
- EN