Combinatorial Ricci flows on surfaces. (English) Zbl 1070.53040

Chow, Bennett; Luo, Feng

J. Differ. Geom. 63, No. 1, 97-129 (2003).

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.

MSC:

53C44

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

Keywords:

Hamilton’s Ricci flow; Thurston’s circle packing on surfaces