Distance difference functions on non-convex boundaries of Riemannian manifolds

TL;DR

This paper proves that a complete Riemannian manifold with boundary can be uniquely reconstructed from boundary distance difference data without boundary restrictions.

Contribution

It establishes a new uniqueness result for Riemannian manifolds using boundary distance difference functions without boundary constraints.

Findings

Manifolds are uniquely determined by boundary distance difference data.

No boundary restrictions are needed for the uniqueness result.

Extends previous results to more general boundary conditions.

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.