Combinatorial Ricci flows on surfaces

Bennett Chow Feng Luo

Algebraic Geometry mathscidoc:1912.43775

Journal of Differential Geometry, 63, (1), 97-129, 2003
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.
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  title={Combinatorial Ricci flows on surfaces},
  author={Bennett Chow, and Feng Luo},
  booktitle={Journal of Differential Geometry},
Bennett Chow, and Feng Luo. Combinatorial Ricci flows on surfaces. 2003. Vol. 63. In Journal of Differential Geometry. pp.97-129.
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