Lorentzian Calderon problem under curvature bounds

• 成果类型: Article
• 署名作者: Alexakis, Spyros; Feizmohammadi, Ali; Oksanen, Lauri
• 署名单位: University of Toronto; University of London; University College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01100-5
• 发表日期: 2022
• 页码: 87-138
• 关键词: INVERSE PROBLEMS; unique continuation; reconstruction; Operators; EQUATIONS; carleman; THEOREMS

摘要

We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying the curvature bounds has a non-empty interior in the sense of arbitrary, smooth perturbations of the metric, whereas all previous results on this problem impose conditions on the metric that force it to be real analytic with respect to a suitably defined time variable. The analogous problem on Riemannian manifolds is called the Calderon problem, and in this case the known results require the metric to be independent of one of the variables. Our approach is based on a new unique continuation result in the exterior region of double null cones. The approach shares features with the classical Boundary Control method, and can be viewed as a generalization of this method to cases where no real analyticity is assumed.