Effondrement des variétés riemanniennes, d’après J. Cheeger, et M. Gromov. (French) Zbl 0551.53020

Sémin. Bourbaki, 36e année, Vol. 1983/84, Exp. No. 618, Astérisque 121/122, 63-82 (1985).
[For the entire collection see Zbl 0542.00005.]
This paper is a well written report on an important new development in Riemannian geometry. The author first explains Gromov’s improvement of Cheeger’s finiteness theorem, the so-called compactness theorem of Gromov [see M. Gromov, Structures métriques pour les variétés riemanniennes (1981; Zbl 0509.53034)]. Then the author explains Cheeger and Gromov’s characterization of collapsing manifolds [see J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, preprint].
Reviewer: G.Thorbergsson


53C20 Global Riemannian geometry, including pinching
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