Combinatorial Ricci flows on surfaces. (English) Zbl 1070.53040

Summary: 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.


53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
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