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Combinatorial Ricci Flows on Surfaces

Bennett Chow·Feng Luo
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Abstract

We show that the analog 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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Bennett Chow, Feng Luo. 2002-11-17. Combinatorial Ricci Flows on Surfaces. https://arxiv.org/abs/math/0211256

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