Ricci Flow method in the existence problem of the K"ahler-Einstein metrics

TL;DR

This paper explains the Ricci flow method for establishing the existence of Kähler-Einstein metrics, detailing calculations and estimates based on foundational works, serving as a seminar lecture note.

Contribution

It provides a detailed exposition of the Ricci flow approach to Kähler-Einstein metrics, including calculations and estimates from key papers, with added explanations.

Findings

Clarifies Ricci flow method in Kähler-Einstein metrics

Includes detailed calculations and estimates

Serves as educational seminar note

Abstract

This note illustrates the Ricci flow method based on the Cao.H.D's paper[1] and Yau.S.T's paper[4], and tries to explain the method in detail, especially in some calculations. Jian Song and Weinkove's note[9] used some other estimates to obtain the result, this paper will explain some of their estimates as well. This note was a seminar lecture note in 2022 summer when the author was giving lectures on the geometry analysis seminar reasearching the Ricci flow method. The part of the imporatnt zero order estimate is going to be added in a few days. The level of the author is limited, if there are any errors, please do not hesitate to advise. Any comments will be grateful.