Convergence of Ricci flow on $R^2$ to plane

TL;DR

This paper establishes conditions under which the Ricci flow on the Euclidean plane exists globally and converges to a flat metric as time approaches infinity.

Contribution

It provides a sufficient condition ensuring global existence and convergence of Ricci flow on R^2 to the flat metric, advancing understanding of geometric flow behavior.

Findings

Ricci flow on R^2 exists globally under certain conditions.

Flow converges to the flat metric at infinity.

Provides a criterion for convergence of Ricci flow.

Abstract

In this paper, we give a sufficient condition such that the Ricci flow in $R^2$ exists globally and the flow converges at $t=\infty$ to the flat metric on $R^2$.