2016/05/20 by Hanming Zhou, Zhou, Hanming
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1605.06257
openalex publication_date 2016/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension ≥ 3 with boundary. We show that one can uniquely determine the conformal factor and the magnetic field near a strictly convex (with respect to the magnetic geodesics) boundary point where the lens data is accessible. We also prove a boundary rigidity result with partial data assuming the lengths of magnetic geodesics joining boundary points near a strictly convex boundary point are known. The local lens rigidity result also leads to a global rigidity result under some strictly convex foliation condition. A discussion of a weaker version of the lens rigidity problem with partial data for general smooth curves is given at the end of the paper.