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We give a simple proof for the rotational symmetry of ancient solutions ofRicci flow on surfaces. As a consequence we obtain a simple proof of someresults of P.Daskalopoulos, R.Hamilton and N.Sesum on the a priori estimatesfor the ancient solutions of Ricci flow on surfaces. We also give a simpleproof for the solution to be a Rosenau solution under some mild conditions onthe solutions of Ricci flow on surfaces.

Rotational symmetry and properties of the ancient solutions of Ricci flow on surfaces