10/19/2007

Weiyong He
UBC

The Calabi flow on K\"ahler surfaces

We discuss the formation of the singularities of the Calabi flow with the assumption of uniform bounded Sobolev constant, in particular on K\"ahler surfaces. On some certain K\"ahler surfaces, we can generalize Tian'c condition to get the Sobolev constant a priori and show there is no bubble formed along the flow. It follows that the convergence of the flow and some new existence result of constant scalar curvature metric on certain K\"ahler class.