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A note on uniformization of Riemann surfaces by Ricci flow

Author(s): Xiuxiong Chen; Peng Lu; Gang Tian
Journal: Proc. Amer. Math. Soc. 134 (2006), 3391-3393.
MSC (2000): Primary 53C44
Posted: June 6, 2006
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Abstract | References | Similar articles | Additional information

Abstract: We clarify that the Ricci flow can be used to give an independent proof of the uniformization theorem of Riemann surfaces.

References:

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H.D. Cao, B. Chow, S.C. Chu and S.T. Yau (editors), Collected papers on Ricci flow. Internat. Press, Somerville, MA (2003). MR 2145154

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B. Chow, On the entropy estimate for the Ricci flow on compact 2-orbifolds. J. Diff. Geom. 33 (1991), 597-600. MR 1094471 (92e:58228)

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B. Chow and D. Knopf, The Ricci flow: An introduction. AMS, Providence, RI (2004).MR 2061425 (2005e:53101)

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X.X. Chen and G. Tian, unpublished notes.

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B. Chow and L.F. Wu, The Ricci flow on compact 2-orbifolds with curvature negative somewhere. Comm. Pure Appl. Math. 44 (1991), 275-286.MR 1090433 (92g:53035)

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R. Hamilton, The Ricci flow on surfaces, Contemp. Math. 71 AMS, Providence, RI (1988), 237-262. MR 0954419 (89i:53029)

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Additional Information:

Xiuxiong Chen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: xxchen@math.wisc.edu

Peng Lu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: penglu@darkwing.uoregon.edu

Gang Tian
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: tian@math.princeton.edu

DOI: 10.1090/S0002-9939-06-08360-2
PII: S 0002-9939(06)08360-2
Keywords: Ricci flow, uniformization of Riemann surfaces
Received by editor(s): May 25, 2005
Received by editor(s) in revised form: June 3, 2005
Posted: June 6, 2006
Additional Notes: The authors were supported in part by NSF research grants.
Communicated by: Richard A. Wentworth
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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