Calculus of Variations and Geometric Measure Theory

E. Paolini - E. Stepanov - Y. Teplitskaya

An example of an infinite Steiner tree connecting an uncountable set

created by stepanov on 22 Jul 2013
modified by paolini on 19 Mar 2016


Published Paper

Inserted: 22 jul 2013
Last Updated: 19 mar 2016

Journal: Adv. Calc. Var.
Volume: 8
Number: 3
Pages: 267–-290
Year: 2015
Doi: 10.1515/acv-2013-0025


We construct an example of a Steiner tree with an infinite number of branching points connecting an uncountable set of points. Such a tree is proven to be a unique solution to a Steiner problem for the given set of points. As a byproduct we get the whole family of explicitly defined finite Steiner trees, which are unique connected solutions of the Steiner problem for some given finite sets of points, and with growing complexity (i.e. the number of branching points).

Keywords: Steiner problem, Steiner minimal tree