Calculus of Variations and Geometric Measure Theory
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R. Choksi - X. Y. Lu

Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D

created by lu on 01 May 2019


Submitted Paper

Inserted: 1 may 2019
Last Updated: 1 may 2019

Year: 2018

ArXiv: 1806.07591 PDF


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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