Combinatorial Calabi flows on surfaces

Details Combinatorial Calabi flows on surfaces Combinatorial Calabi flows on surfaces

2012-04-13

arxiv.org/abs/1204.2930v1

Mathematics

Differential Geometry

22 pages

Scientific paper

We introduce the {\em combinatorial Calabi flow} on the space of all circle packing metrics associated to a triangulated surface, in terms of an ODE system. It is the negative gradient flow of discrete Calabi energy and the analog of smooth Calabi flow first defined by E.Calabi\cite{CA1}\cite{CA2}. We found that this discrete flow exists for all time and converges to Thurston's circle packing metric, which induces a constant discrete curvature, similar to the combinatorial Ricci flow on surfaces introduced by Bennett Chow and Feng Luo\cite{CL1}, except for convergence rate.

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