Inverse problems for Einstein manifolds
Abstract
We show that the DirichlettoNeumann 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1136
 Bibcode:
 2007arXiv0710.1136G
 Keywords:

 Mathematics  Differential Geometry;
 35R30
 EPrint:
 Corrected version