Inverse problems for Einstein manifolds

Colin Guillarmou; Antonio Sa Barreto

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arXiv · 0710.1136

Inverse problems for Einstein manifolds

Colin Guillarmou·Antonio Sa Barreto

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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.

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BibTeX RIS

Colin Guillarmou, Antonio Sa Barreto. 2008-10-06. Inverse problems for Einstein manifolds. https://arxiv.org/abs/0710.1136

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