A note on existence of exhaustion functions and its applications

TL;DR

This paper proves an existence result for exhaustion functions using Tam's method and applies it to establish short-time Ricci flow existence and explore Yau's uniformization conjecture.

Contribution

It introduces a new existence theorem for exhaustion functions and applies it to key problems in geometric analysis, including Ricci flow and Yau's conjecture.

Findings

Proved an existence theorem for exhaustion functions.

Established short-time existence of Ricci flow.

Provided insights into Yau's uniformization conjecture.

Abstract

In this note, we prove an existence result on exhaustion functions adapting the method by L.-F. Tam. Then we apply it to prove short-time existence of Ricci flow and study Yau's uniformization conjecture using similar method as Fei He and Lee-Tam.