Convergence of Ricci flow on ${\mathbb{R}}^2$ to flat space

Abstract

We prove that, starting at an initial metric $g(0)=e^{2u_0}(d{x}^2+d{y}^2)$ on ${\mathbb{R}}^2$ with bounded scalar curvature and bounded $u_0$, the Ricci flow ${\partial }_{t}g(t)=-R_{g(t)}g(t)$ converges to a flat metric on ${\mathbb{R}}^2$.

9 pages