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

We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of Daskalopoulos, Hamilton and Sesum on the a priori estimates for the ancient solutions of Ricci flow on surfaces. We also give a simple proof for the solution to be a Rosenau solution under some mild conditions on the solutions of Ricci flow on surfaces.