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

James Isenberg; Mohammad Javaheri

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arXiv · 0908.2264

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

James Isenberg·Mohammad Javaheri

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Abstract

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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James Isenberg, Mohammad Javaheri. 2009-08-16. Convergence of Ricci flow on $\mathbb{R}^2$ to flat space. https://arxiv.org/abs/0908.2264

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