Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D
| Autor: | Rustum Choksi, Xin Yang Lu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Conjecture Computation media_common.quotation_subject 010102 general mathematics Structure (category theory) Statistical and Nonlinear Physics Computer Science::Computational Geometry Infinity 01 natural sciences Simple (abstract algebra) 0103 physical sciences Convex optimization 010307 mathematical physics 0101 mathematics Centroidal Voronoi tessellation Voronoi diagram Mathematical Physics Mathematics media_common |
| Zdroj: | Communications in Mathematical Physics. 377:2429-2450 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-020-03789-y |
| Popis: | 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 as the number of generators tends to infinity. Combined with an approach of Gruber in 2D, these bounds reduce the resolution of the 3D Gersho’s conjecture to a finite, albeit very large, computation of an explicit convex problem in finitely many variables. |
| Databáze: | OpenAIRE |
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