Ricci Curvature and Differentiable rigidity
by
Gérard Besson
Université de Grenoble I, FRANCE
Coauthors: Gilles Courtois and Sylvestre Gallot

We shal use the construction of maps given in the educational talk to prove a differentiable rigidity theorem. More precisely we shall consider a manifold which is homotopically equivalent to an hyperbolic manifold (i.e of sectional curvature equal to -1). There exists a constant e such that if the manifold carries a metric whose Ricci curvature is bounded below by n-1 and whose volume is less than e then it is diffeomorphic to the hyperbolic manifold.

Date received: December 18, 2006