## Differential and Integral Equations

### Global existence and uniqueness of solutions of the Ricci flow equation

Shu-Yu Hsu

#### Abstract

In this paper we will prove the global existence and uniqueness of solutions of the Ricci flow equation on $R^2$ $u_t=\Delta \text{ log }u$, $u>0$, in $R^2\times (0,\infty)$, $u(x,0) =u_0(x)$ for $x\in R^2$, satisfying the inequality $u_t\le u/t$ in $R^2\times (0,\infty)$ and the condition $\liminf_{r\to\infty}$ log $u(x,t)/\text{log }r\ge -2$ uniformly on any compact subset of $(0,\infty)$ as $r=|x|\to\infty$ for any $u_0\not\in L^1(R^2)$, $u_0\ge 0$, satisfying $u_0\in L_{loc}^p(R^2)$ for some $p>1$.

#### Article information

Source
Differential Integral Equations, Volume 14, Number 3 (2001), 305-320.

Dates
First available in Project Euclid: 21 December 2012