Finiteness of $\pi_1$ and geometric inequalities in almost positive Ricci curvature.
Résumé
We show that complete $n$-manifolds whose part of Ricci curvature less than a positive number is small in $L^p$ norm (for $p>n/2$) have bounded diameter and finite fundamental group. On the contrary, complete metrics with small $L^{n/2}$-norm of the same part of the Ricci curvature are dense in the set of metrics of any compact differentiable manifold.
Domaines
Géométrie différentielle [math.DG]
Origine : Fichiers produits par l'(les) auteur(s)