Séminaire Gaston Darboux :

Le 23 septembre 2011 à 11:15 - salle 431

Présentée par Coda Marques Fernando - IMPA Rio de Janeiro

Rigidity of min-max minimal spheres in three-manifolds

In this talk we will consider min-max minimal surfaces in three-manifolds and describe some rigidity results. For instance, we will discuss the proof that any metric on a 3-sphere which has scalar curvature greater than or equal to 6 and is not round must have an embedded minimal sphere of area strictly smaller than $4\pi$ and index at most one. We will also mention some sharp estimates for the width in the case of positive Ricci curvature. The proofs use Ricci flow. This is joint work with Andre Neves.