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