March 27, 2008

Simon Brendle (Stanford University)

Title: A sufficient condition for the convergence of the Ricci flow in higher dimensions

Abstract: In a recent joint work with Richard Schoen, we proved that the Ricci flow deforms a metric with pointwise $1/4$-pinched sectional curvature to a metric of constant curvature. We will discuss how the $1/4$-pinching condition can be replaced by the weaker condition that $M \times \mathbb{R}$ has positive isotropic curvature. The latter condition implies positive Ricci curvature, but is weaker than $2$-positive curvature operator.