  We give a simple proof of an extension of the existence results of Ricci flow
of G.Giesen and P.M.Topping [GiT1],[GiT2], on incomplete surfaces with bounded
above Gauss curvature without using the difficult Shi's existence theorem of
Ricci flow on complete non-compact surfaces and the pseudolocality theorem of
G.Perelman [P1] on Ricci flow. We will also give a simple proof of a special
case of the existence theorem of P.M.Topping [T] without using the existence
theorem of W.X.Shi [S1].
