Combinatorial Ricci Flows on Surfaces
Copyright policy )Combinatorial Ricci Flows on Surfaces
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.
25 pages, no figures
- University of California, San Diego United States
- University of California, San Diego United States
- Rutgers University New Brunswick United States
- University of California, San Francisco United States
Mathematics - Differential Geometry, Mathematics - Geometric Topology, 52C26, Differential Geometry (math.DG), Thurston's circle packing on surfaces, Hamilton's Ricci flow, FOS: Mathematics, Geometric Topology (math.GT), 53C44; 52C26, 53C44, Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Mathematics - Differential Geometry, Mathematics - Geometric Topology, 52C26, Differential Geometry (math.DG), Thurston's circle packing on surfaces, Hamilton's Ricci flow, FOS: Mathematics, Geometric Topology (math.GT), 53C44; 52C26, 53C44, Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).251 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 1% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!