A ug 2 00 8 The Calabi flow on Kähler Surfaces with bounded Sobolev constant ( I )

3 The evolution formulas 13 4 ALE cextK metrics 18 5 Formation of singularities with a uniformly bounded Sobolev constant 19 5. 6 The Calabi flow on toric Fano surfaces 28 7 Appendix: calculation case by case 29 7. 1 Introduction In [11], E. Calabi proposed to deform a Kähler metric in the direction of the Levi-Hessian of its scalar curvature. This is a 4th… (More)