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arXiv · 0806.0632

The existence problem for Steiner networks in strictly convex domains

Alex Freire
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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.

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Alex Freire. 2008-06-03. The existence problem for Steiner networks in strictly convex domains. https://arxiv.org/abs/0806.0632

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