Journal of Differential Geometry

Combinatorial Ricci Flows on Surfaces

Bennett Chow and Feng Luo

Abstract

We show that the analogue of Hamilton's Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston's circle packing on surfaces. As a consequence, a new proof of Thurston's existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings.

Article information

Source
J. Differential Geom., Volume 63, Number 1 (2003), 97-129.

Dates
First available in Project Euclid: 1 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1080835659

Digital Object Identifier
doi:10.4310/jdg/1080835659

Mathematical Reviews number (MathSciNet)
MR2015261

Zentralblatt MATH identifier
1070.53040

Citation

Chow, Bennett; Luo, Feng. Combinatorial Ricci Flows on Surfaces. J. Differential Geom. 63 (2003), no. 1, 97--129. doi:10.4310/jdg/1080835659. https://projecteuclid.org/euclid.jdg/1080835659


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