“Ricci flow and the classification of 1/4-pinched manifolds”
Simon Brendle, Stanford University

Abstract:
I will describe the recent classification (joint with Rick Schoen) of manifolds with pointwise 1/4-pinched curvature. This proof employs the Ricci flow, but the curvature condition we consider first arose from consideration of the index form for minimal surfaces. I will also discuss the borderline case of manifolds with weakly 1/4-pinched curvature. This relies on a new strong maximum principle for the Ricci flow.