Inverse problems for Einstein manifolds

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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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Differential Geometry, 35R30

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http://salesiana.dossiersoluciones.com/handle/123456789/170582

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.1136
 http://arxiv.org/abs/0710.1136

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arXiv