Local solution and extension to the Calabi flow

Abstract

We consider the local solution to the Calabi flow for C^αinitial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\infty sense. This can be viewed as obtaining higher order derivative estimates from second order derivatives for a fourth order nonlinear equation.

11 pages; Proof of Theorem 2.1 is rewritten

References in corpus (2)

• The Calabi flow on Kähler surface with bounded Sobolev constant
• The Calabi functional on a ruled surface

Cited by in corpus (1)

• Stability of Calabi flow near an extremal metric