On the stable recovery of a metric from the hyperbolic DN map with incomplete data

TL;DR

This paper demonstrates that close hyperbolic Dirichlet to Neumann maps imply identical lens data for Riemannian metrics, leading to local uniqueness in recovering a conformal factor under certain conditions.

Contribution

It establishes a link between boundary measurements and lens data, proving local uniqueness in recovering a conformal factor from incomplete boundary data.

Findings

Close hyperbolic DN maps imply identical lens data.

Uniqueness of local recovery of conformal factors.

Results apply under specific boundary coincidence conditions.

Abstract

We show that given two hyperbolic Dirichlet to Neumann maps associated to two Riemannian metrics of a Riemannian manifold with boundary which coincide near the boundary are close then the lens data of the two metrics is the same. As a consequence, we prove uniqueness of recovery a conformal factor (sound speed) locally under some conditions on the latter.