On the Calabi flow

Details On the Calabi flow On the Calabi flow

2006-03-21

arxiv.org/abs/math/0603523v3

Mathematics

Differential Geometry

A recent updated version with some correction

Scientific paper

We first give a precise statement on the short time existence of the Calabi flow and prove a stability result: any metric near a constant scalar curvature metric will flow to this cscK metric exponentially fast. Secondly, we prove that a compactness theorem in space of the kahler metrics given unifrom Ricci bound and potential bound. As an application, we prove the Calabi flow can be extended once Ricci curvature stays uniformly bounded. Lastly, we prove a removing-sigularity result about a weak constant scalar curveture metric in a punctured ball. One of the main difficulties is that the metric is not assumed to be smooth outside of the singular point.

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