On Four-dimensional Noncollapsed Steady Ricci Solitons

Zilu Ma, Rutgers University

Abstract: Steady Ricci Solitons may arise as singularity models of the Ricci flow and they are essential to the singularity analysis in order to achieve any topological applications using surgeries, particularly in dimension 4. In this talk, we shall present some results on four-dimensional noncollapsed steady gradient Ricci solitons in some recent joint works. We first classify the tangent flows at infinity in dimension four. With the classification at infinity, we give a classification of Kaehler steady solitons. Under the assumption of positive curvature, we present some recent results on rough geometric asymptotics and precise analytic asymptotics.