2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227472We 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 rewrittenDifferential GeometryAnalysis of PDEstext