Analysis on Manifolds and the Ricci Curvature

  • Sylvestre Gallot
  • Dominique Hulin
  • Jacques Lafontaine
Part of the Universitext book series (UTX)

Abstract

Analysis on Riemannian manifolds stems from the following simple fact: the classical Laplace operator has an exact Riemannian analog. Indeed, the properties of the Laplacian on a bounded Euclidean domain and on a compact Riemannian manifold are very similar, and so are the techniques of proofs. We can say that the difficulties of the latter case, compared with the former, are essentially conceptual.

Keywords

Riemannian Manifold Ricci Curvature Isoperimetric Inequality Compact Riemannian Manifold Geodesic Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 1
  • Jacques Lafontaine
    • 2
  1. 1.Ecole Polytechnique, Unité de Recherche Associée du CNRS D 0169Centre de MathématiquesPalaiseau CedexFrance
  2. 2.Départment de Mathématiques, GETODIM - Unité de Recherche Associée du CNRS 1407Université de MontpellierMontpellier Cedex 5France

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