Distance difference functions on non-convex boundaries of Riemannian manifolds

2020/08/30 by Sergei Ivanov, Ivanov, Sergei
Mathematics · #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2008.13153

Abstract

We show that a complete Riemannian manifold with boundary is uniquely determined, up to an isometry, by its distance difference representation on the boundary. Unlike previously known results, we do not impose any restrictions on the boundary.

Related

• Distance difference representations of Riemannian manifolds
• Convexity of the distance function to convex subsets of Riemannian manifolds
• Problems of unique determination of domains by the relative metrics on\n their boundaries
• Determination of a Riemannian manifold from the distance difference functions
• Two dimensional compact simple Riemannian manifolds are boundary distance rigid