A Simple Ricci Flow Proof of the Uniformization Theorem
Differential Geometry
2024-08-27 v6 Complex Variables
Abstract
In this note, we provide a very simple proof of the uniformization theorem of Riemann surfaces by Ricci flow. The argument builds on a refinement of Hamilton's isoperimetric estimate for the Ricci flow on the two-sphere.
Keywords
Cite
@article{arxiv.2404.01980,
title = {A Simple Ricci Flow Proof of the Uniformization Theorem},
author = {Yucheng Ji},
journal= {arXiv preprint arXiv:2404.01980},
year = {2024}
}
Comments
There is a flaw in the proof of Theorem 3.3 that the A at t=0 and A at t=T cannot be guaranteed to be identical, thus the key inequality fails