Calabi Symmetry and the Continuity Method

Abstract

We study the convergence and curvature blow up of La Nave and Tian's continuity method on a generalised Hirzebruch surface. We show that the Gromov-Hausdorff convergence is similar to that of the Kahler-Ricci flow and obtain curvature estimates. We also show that a general solution to the continuity method either exist or all times, or the scalar curvature blows up. This behavior is known to be exhibited by the Kahler-Ricci flow.