Sur une in�galit� isop�rim�trique qui g�n�ralise celle de Paul L�vy-Gromov

Diameter pinching in almost positive Ricci curvature

“…The same technic as in [5] can be used to prove that manifolds with almost positive Ricci curvature and λ 1 is close to n have a diameter close to π (see [12]). …”

On Gromov′s theorem and L 2‐Hodge decomposition

“…[5] and the references therein). Furthermore, an explicit η has been provided by Gallot in [12,13] for such a theorem to hold.…”

“…Let ·, · x denote the inner product on Ω x , and for f ∈ ᏹ, let |f |(x) = |f (x)| x := f (x), f (x) In the case where V = 0, it was proved by Bérard et al [5] that there is η > 0 depending only on l, KD 2 ,…”

“…This enables one to estimate b p using analytic approaches. A very famous result in the literature is the following Gromov's theorem [15] (see [5] for extensions to Riemannian vector bundles). Throughout the paper, let M be a connected complete Riemannian manifold of dimension d.…”

Un nouveau résultat de pincement de la première valeur propre du laplacien et conjecture du diamètre pincé

“…[8]) ainsi que par Bérard, Besson et Gallot (cf. [2]). Et c'est ainsi que Croke prouve son théorème (réponse à la question II) en utilisant le théorème de Grove-Shiohama.…”