Ricci Flow on Open Surface

J. Math. Sci. Univ. Tokyo
Vol. 20 (2013), No. 3, Page 435–444.

Zhu, Xiaorui
Ricci Flow on Open Surface
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In this note, we study the normalized Ricci flow with incomplete initial metric. By an approximation method initiated by Giesen and Topping very recently, we show such flow with suitable initial value always converges exponentially to a metric with constant Gaussian curvature. If moreover the initial metric is complete, the flow converges to the hyperbolic metric. Applications of Ricci flow to uniformization of Riemann surfaces are also considered.

Keywords: Ricci flow, incomplete surface, uniformization theorem.

Mathematics Subject Classification (2010): Primary 53C44; Secondary 30F10.
Mathematical Reviews Number: MR3156988

Received: 2013-08-09