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

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

2009-08-16

arxiv.org/abs/0908.2264v1

Mathematics

Differential Geometry

9 pages

Scientific paper

We prove that, starting at an initial metric $g(0)=e^{2u_0}(dx^2+dy^2)$ 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 $\mathbb{R}^2$.

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