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A note on uniformization of Riemann surfaces by Ricci flow. (English) Zbl 1113.53042
In this note the authors give a novel proof of the result that if \(g\) is a gradient shrinking Ricci soliton on a closed surface \(\Sigma^2\), then \(g\) has positive constant curvature. The novelty is that the authors prove it without using the uniformization theorem.

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
Full Text: DOI arXiv
[1] H. D. Cao, B. Chow, S. C. Chu, and S. T. Yau , Collected papers on Ricci flow, Series in Geometry and Topology, vol. 37, International Press, Somerville, MA, 2003. · Zbl 1108.53002
[2] Bennett Chow, The Ricci flow on the 2-sphere, J. Differential Geom. 33 (1991), no. 2, 325 – 334. · Zbl 0734.53033
[3] Bennett Chow, On the entropy estimate for the Ricci flow on compact 2-orbifolds, J. Differential Geom. 33 (1991), no. 2, 597 – 600. · Zbl 0734.53034
[4] Bennett Chow and Dan Knopf, The Ricci flow: an introduction, Mathematical Surveys and Monographs, vol. 110, American Mathematical Society, Providence, RI, 2004. · Zbl 1086.53085
[5] X.X. Chen and G. Tian, unpublished notes.
[6] Bennett Chow and Lang-Fang Wu, The Ricci flow on compact 2-orbifolds with curvature negative somewhere, Comm. Pure Appl. Math. 44 (1991), no. 3, 275 – 286. · Zbl 0745.58047 · doi:10.1002/cpa.3160440302 · doi.org
[7] Richard S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz, CA, 1986) Contemp. Math., vol. 71, Amer. Math. Soc., Providence, RI, 1988, pp. 237 – 262. · doi:10.1090/conm/071/954419 · doi.org
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