an:04046585
Zbl 0642.53047
Bavard, C.
Courbure presque n??gative en dimension 3. (Almost negative curvature in dimension 3)
FR
Compos. Math. 63, 223-236 (1987).
00153488
1987
j
53C20
diameter; volume; almost negatively curved metrics; curvature
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. \textit{P. Buser} and \textit{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.
K.Grove