Inverse problems for Einstein manifolds

2007/10/05 by Colin Guillarmou, Guillarmou, Colin, Antônio Sá Barreto +1 · 3 citations
Mathematics · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.0710.1136

Abstract

We show that the Dirichlet-to-Neumann operator of the Laplacian on an open subset of the boundary of a connected compact Einstein manifold with boundary determines the manifold up to isometries. Similarly, for connected conformally compact Einstein manifolds of even dimension n+1, we prove that the scattering matrix at energy n on an open subset of its boundary determines the manifold up to isometries.

Citations

• Determining anisotropic real‐analytic conductivities by boundary measurements
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Cited by

• Invisibility and Inverse Problems
• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography
• On the interplay between inverse scattering for asymptotically hyperbolic manifolds and the Calderón problem for the Conformal Laplacian

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