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Courbure presque négative en dimension 3. (Almost negative curvature in dimension 3). (French) Zbl 0642.53047
The following striking theorem is proved: Any closed orientable 3- manifold, M, admits a riemannian metric with curve(M)$$\leq 1$$, diam(M)$$\leq \epsilon$$, and Vol $$M\leq \epsilon$$, for any $$\epsilon >0$$. The first construction of this kind was given by Gromov in the case $$M=S^ 3$$ [cf. P. Buser and D. Gromoll, Gromov’s examples of almost negatively curved metrics on $$S^ 3$$ (to appear)]. In these examples the lower bound for the curvature goes to -$$\infty$$. This is indeed necessary as was shown recently by Fukaya and Yamaguchi.
Reviewer: K.Grove

MSC:
 53C20 Global Riemannian geometry, including pinching
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References:
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