Periodic Steiner networks minimizing length
Differential Geometry
2018-04-26 v2 Combinatorics
Abstract
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 domain of 3-space with the same volume. The minimizer is the so-called srs network with quotient the complete graph on four vertices . The network spans the body centred cubic lattice and is related to the gyroid triply periodic surface.
Keywords
Cite
@article{arxiv.1705.02471,
title = {Periodic Steiner networks minimizing length},
author = {Jerome Alex and Karsten Grosse-Brauckmann},
journal= {arXiv preprint arXiv:1705.02471},
year = {2018}
}
Comments
22 pages, 12 figures. Some results added to Section 2 which make Theorem A more general. Otherwise minor changes