The existence problem for Steiner networks in strictly convex domains
Differential Geometry
2008-06-05 v1
Abstract
We consider the existence problem for `Steiner networks' (trivalent graphs with 120 degree angles at each junction) in strictly convex domains, with `Neumann' boundary conditions (orthogonal intersection with the domain boundary.) For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence; in addition, in each case explicit examples of nonexistence are given.
Keywords
Cite
@article{arxiv.0806.0632,
title = {The existence problem for Steiner networks in strictly convex domains},
author = {Alex Freire},
journal= {arXiv preprint arXiv:0806.0632},
year = {2008}
}
Comments
submitted September 2006, accepted for journal publication November 2007