Advertisement

Geometric & Functional Analysis GAFA

, Volume 2, Issue 2, pp 221–224 | Cite as

A heat semigroup approach to concentration on the sphere and on a compact Riemannian manifold

  • M. Ledoux
Article

Abstract

We give a simple proof of the Lévy concentration of measure phenomenon on the sphere and on a compact Riemannian manifold with strictly positive Ricci curvature using the heat semigroup and Bochner's formula.

Keywords

Riemannian Manifold Simple Proof Ricci Curvature Compact Riemannian Manifold Heat Semigroup 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BE]
    D. Bakry, M. Emery, Diffusions hypercontractives. Séminaire de Probabilités XIX, Springer Lecture Notes in Math. 1123 (1985), 175–206.Google Scholar
  2. [G]
    M. Gromov, Paul Lévy's isoperimetric inequality. Publication de l'I.H.E.S. (1980).Google Scholar
  3. [GHL]
    S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer-Verlag (1987).Google Scholar
  4. [GM]
    M. Gromov, V. D. Milman, A topological application of the isoperimetric inequality, Amer. J. Math. 105 (1983), 843–854.Google Scholar
  5. [L]
    P. Lévy, Problèmes concrets d'analyse fonctionelle, Gauthier-Villars (1951).Google Scholar
  6. [MS]
    V. D. Milman, G. Schechtman, Asymptotic theory of finite dimensional normed spaces. Springer Lecture Notes in Math. 1200 (1986).Google Scholar
  7. [P]
    G. Pisier, Probabilistic methods in the geometry of Banach spaces. Probability and Analysis, Varenna (Italy) 1985. Springer Lecture Notes in Math. 1206 (1986), 167–241.Google Scholar

Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • M. Ledoux
    • 1
    • 2
  1. 1.Institut de Recherche Mathématique Avancée Laboratoire associé au C.N.R.S.Université Louis-PasteurStrasbourgFrance
  2. 2.Equipe d'Analyse Unité Associée au C.N.R.S.Université de Paris VIParisFrance

Personalised recommendations