Periodic Steiner Networks Minimizing Length

被引：1

作者：

Alex, Jerome ^{[1
]}

Grosse-Brauckmann, Karsten ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2023年 / 70卷 / 04期

关键词：

Triply periodic network; Length minimizer; srs network; Laves network; Gyroid; CURVATURE; CHEMISTRY;

D O I：

10.1007/s00454-023-00576-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study a problem of geometric graph theory: We determine the triply periodic graph in Euclidean 3-space which minimizes length among all graphs spanning a fundamental domainwith the same volume. Theminimizer is the so-called srs network with quotient the complete graph on four vertices K-4. For comparison we consider a competing topological class, also with a quotient on four vertices, and determine the minimizing ths networks.

引用

页码：1145 / 1168

页数：24

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