The Schläfli Formula in Einstein Manifolds with Boundary

  title={The Schläfli Formula in Einstein Manifolds with Boundary},
  author={Jean-Marc Schlenker},
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
Highly Cited
This paper has 20 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 20 references

Einstein manifolds with convex boundaries

  • J.-M. Schlenker
  • Prépublication no. 98-12, Université de Paris-Sud
  • 1998
1 Excerpt

Schläfli formula for Einstein manifolds

  • I. Rivin, J-M. Schlenker
  • IHES Preprint
  • 1998
1 Excerpt

A Schläfli formula for simplices in semi-Riemannian hyperquadrics

  • E. Suarez-Peiró
  • Gauss-Bonnet formulas for simplices in the de…
  • 1997
1 Excerpt

Métriques d’Einstein asymptotiquement symétriques

  • O. Biquard
  • Prépublication no. 9724, Ecole Polytechnique
  • 1997
1 Excerpt

Journal of Differential Geometry

  • David D. Bleecker. Volume increasing isometric deformati polyhedra
  • 43:505–526,
  • 1996


  • J. Milnor. The Schläfli differential equality. In Col papers
  • 1. Publish or Perish,
  • 1994
1 Excerpt


  • D. V. Alekseevskij, E. B. Vinberg, A. S. Solodovnikov. Geometry of Spaces of Constant Curvature, Encyclopaedia of Math. Sci.
  • Springer, Berlin,
  • 1993
1 Excerpt

Géométrie différentielle: variétés

  • M. Berger, B. Gostiaux
  • courbes et surfaces. Presses universitaires de…
  • 1993


  • C. R. Graham, J. M. Lee. Einstein metrics with prescribed conformal ball
  • Math., 87:186–225,
  • 1991
1 Excerpt

Similar Papers

Loading similar papers…