Journal of Geometric Analysis

, Volume 19, Issue 4, pp 809–816 | Cite as

Convergence of Ricci Flow on ℝ2 to Flat Space



We prove that, starting at an initial metric \(g(0)=e^{2u_{0}}(dx^{2}+dy^{2})\) on ℝ2 with bounded scalar curvature and bounded u0, the Ricci flow tg(t)=−Rg(t)g(t) converges to a flat metric on ℝ2.


Ricci flow Convergence Fast diffusion Conformally flat 

Mathematics Subject Classification (2000)

53C44 35K55 


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Copyright information

© Mathematica Josephina, Inc. 2009

Authors and Affiliations

  1. 1.University of OregonEugeneUSA
  2. 2.Trinity CollegeHartfordUSA

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