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In this paper, we establish a framework for the analysis of linear parabolicequations on conical surfaces and use them to study the conical Ricci flow. Inparticular, we prove the long time existence of the conical Ricci flow forgeneral cone angle and show that this solution has the optimal regularity,namely, the time derivatives of the conformal factor are bounded and for eachfixed time, the conformal factor has an explicit asymptotic expansion near thecone points.

Analysis aspects of Ricci flow on conical surfaces