1 Combinatorial scalar curvature andrigidity of ball packings
نویسندگان
چکیده
منابع مشابه
Combinatorial Scalar Curvature and Rigidity of Ball Packings
Let M be a triangulated three-dimensional manifold. In this paper we define a combinatorial analogue of scalar curvature for M, and also a combinatorial 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 combinato...
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In his proof of Andreev’s theorem, Thurston in [1] introduced a conformal geometric structure on two dimensional simplicial complexes which is an analogue of a Riemannian metric. He then used a version of curvature to prove the existence of circle-packings (see also Marden-Rodin [2] for more exposition). Techniques very similar to elliptic partial differential equation techniques were used by Y...
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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 nonsin...
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In this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-dimensional spaces of constant curvature. The topics discussed are as follows: Hadwiger numbers of convex bodies and kissing numbers of spheres; Touching numbers of convex bodies; Newton numbers of convex bodies; One-sided Hadwiger and kissing numbers; Contact graphs of finite packings ...
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