Local solution and extension to the Calabi flow

Details Local solution and extension to the Calabi flow Local solution and extension to the Calabi flow

2009-04-06

arxiv.org/abs/0904.0978v2

Mathematics

Differential Geometry

11 pages; Proof of Theorem 2.1 is rewritten

Scientific paper

We consider the local solution to the Calabi flow for C^\alpha initial
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.

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