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COMBINATORIAL SCALAR CURVATURE i Combinatorial scalar curvature and rigidity of ball packings

By Daryl Cooper And, Daryl Cooper and Igor Rivin


this paper we define a combinatorial analogue of scalar curvature for Jk/3 and also a combi- natorial analogue of conformal deformation of the metric. We further define a functional S on the combinatorial conformal deformation space, show that S is concave, and show that critical points of S correspond precisely to metrics of constant combinatorial scalar curvature on Jk/3. These results are then applied to showing rigidity of ball packings with prescribed combinatorics (the con- cepts are quite similar to Colin de VerdibreWs work on circle packing of surfaces [2]. See also [6] for a related variational argument

Year: 2007
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