Journal Articles Advances in Calculus of Variation Year : 2015

AN EXAMPLE OF AN INFINITE STEINER TREE CONNECTING AN UNCOUNTABLE SET

Abstract

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 the 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).

Fichier principal
Vignette du fichier
paostetepl12-steiner-eng1.pdf (252.22 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04825897 , version 1 (08-12-2024)

Identifiers

Cite

Emanuele Paolini, Eugene Stepanov, Yana Teplitskaya. AN EXAMPLE OF AN INFINITE STEINER TREE CONNECTING AN UNCOUNTABLE SET. Advances in Calculus of Variation, 2015, 8 (3), pp.267-290. ⟨10.1515/acv-2013-0025⟩. ⟨hal-04825897⟩

Collections

CNRS
9 View
2 Download

Altmetric

Share

More