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

2015/05/12 by Stefanov, Plamen, Uhlmann, Gunther, Vasy, Andras · 1 citation
#35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.02853

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.

Cited by

• Stability of Gel'fand's inverse interior spectral problem for Schrödinger operators

Related

• Boundary rigidity with partial data
• Stable recovery of a metric tensor from the partial hyperbolic Dirichlet to Neumann map
• Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map
• Local lens rigidity with incomplete data for a class of non-simple Riemannian manifolds
• Rigidity in the Lorentzian Calderón problem with formally determined data