Local solution and extension to the Calabi flow
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math.DG
math.AP
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flowcalabiorderlocalsolutionalongalphabounded
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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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