The Schläfli Formula in Einstein Manifolds with Boundary

@inproceedings{Schlenker1999TheSF,
  title={The Schläfli Formula in Einstein Manifolds with Boundary},
  author={Jean-Marc Schlenker},
  year={1999}
}
We give a smooth analogue of the classical Schläfli formula, relating the variation of the volume bounded by a hypersurface moving in a general Einstein manifold and the integral of the variation of the mean curvature. We extend it to variations of the metric in a Riemannian Einstein manifold with boundary, and apply it to Einstein cone-manifolds, to isometric deformations of Euclidean hypersurfaces, and to the rigidity of Ricci-flat manifolds with umbilic boundaries. Résumé. On donne un… CONTINUE READING
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