English

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

R2 v1 2026-06-21T10:47:11.814Z