Calculus of Variations and Geometric Measure Theory

An example of an infinite Steiner tree connecting an uncountable set

Yana Teplitskaya

created by dicastro on 15 Nov 2013

20 nov 2013 -- 17:00   [open in google calendar]

Aula Seminari - Department of Mathematics, University of Pisa


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)