A combinatorial Yamabe flow in three dimensions |
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Authors: | David Glickenstein |
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Institution: | Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA |
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Abstract: | A combinatorial version of Yamabe flow is presented based on Euclidean triangulations coming from sphere packings. The evolution of curvature is then derived and shown to satisfy a heat equation. The Laplacian in the heat equation is shown to be a geometric analogue of the Laplacian of Riemannian geometry, although the maximum principle need not hold. It is then shown that if the flow is nonsingular, the flow converges to a constant curvature metric. |
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Keywords: | Curvature flow Yamabe flow Sphere packing Laplacian Discrete Riemannian geometry |
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