Normalized Ricci flow on nonparabolic surfaces

TL;DR

This paper investigates the normalized Ricci flow on nonparabolic surfaces with scalar curvature approaching -1, demonstrating convergence to a constant curvature metric using Green's function estimates.

Contribution

It extends Ricci flow analysis to nonparabolic surfaces and introduces a Green's function estimate as a key tool for convergence proof.

Findings

Flow converges to a metric of constant scalar curvature -1

Green's function estimate is established for nonparabolic surfaces

Method adapts Hamilton's approach to a broader class of surfaces

Abstract

This paper studies normalized Ricci flow on a nonparabolic surface, whose scalar curvature is asymptotically -1 in an integral sense. By a method initiated by R. Hamilton, the flow is shown to converge to a metric of constant scalar curvature -1. A relative estimate of Green's function is proved as a tool.