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

TL;DR

This paper provides simplified proofs for the rotational symmetry and certain properties of ancient solutions to Ricci flow on surfaces, clarifying previous results and conditions for specific solutions.

Contribution

It introduces simplified proofs for symmetry and properties of ancient Ricci flow solutions on surfaces, extending understanding of their structure and estimates.

Findings

Ancient solutions of Ricci flow on surfaces are rotationally symmetric.

Established a priori estimates for these solutions.

Identified conditions under which solutions are Rosenau solutions.

Abstract

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 P.Daskalopoulos, R.Hamilton and N.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.