三维最优Voronoi网格几何复杂度的界
Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D
摘要：
3D中的Gersho猜想断言了最优质心Voronoi镶嵌的渐近周期性和结构。这个相对简单的结晶问题至今仍是一个悬而未决的问题。我们证明了边界的几何复杂性的最佳质心Voronoi镶嵌，结合格鲁伯在2D中介绍的方法，减少分辨率的3D Gersho的猜想一个有限的（虽然大）计算的显式凸问题在许多变量。
英文摘要：
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of optimal centroidal Voronoi tessellations which, combined with an approach introduced by Gruber in 2D, reduce the resolution of the 3D Gersho's conjecture to a finite (albeit large) computation of an explicit convex problem in finitely many variables.
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