Inverse problems for Einstein manifolds

Details Inverse problems for Einstein manifolds Inverse problems for Einstein manifolds

2007-10-05

arxiv.org/abs/0710.1136v2

Mathematics

Differential Geometry

Corrected version

Scientific paper

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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