Local solution and extension to the Calabi flow
Abstract
Description
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
11 pages; Proof of Theorem 2.1 is rewritten