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Ricci flow on surfaces with cusps

Lizhen Ji·Rafe Mazzeo·Natasa Sesum
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Abstract

We consider the normalized Ricci flow $\del_t g = (ρ- R)g$ with initial condition a complete metric $g_0$ on an open surface $M$ where $M$ is conformal to a punctured compact Riemann surface and $g_0$ has ends which are asymptotic to hyperbolic cusps. We prove that when $χ(M) < 0$ and $ρ< 0$, the flow $g(t)$ converges exponentially to the unique complete metric of constant Gauss curvature $ρ$ in the conformal class.

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Lizhen Ji, Rafe Mazzeo, Natasa Sesum. 2009-05-11. Ricci flow on surfaces with cusps. https://arxiv.org/abs/math/0703357

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