Another proof of Ricci flow on incomplete surfaces with bounded above Gauss curvature

TL;DR

This paper presents simplified proofs for the existence of Ricci flow on incomplete surfaces with bounded above Gauss curvature, avoiding complex theorems previously used in the field.

Contribution

It provides more accessible proofs for Ricci flow existence on incomplete surfaces, extending prior results without relying on Shi's or Perelman's advanced theorems.

Findings

Simplified proof of Ricci flow existence on incomplete surfaces

Extension of Giesen and Topping's results without Shi's theorem

Proof of a special case of Topping's existence theorem

Abstract

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].