E. I. Stepanova, “Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, Number 2,Pages <nobr>48

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Short notes

Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane

E. I. Stepanova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Bifurcation diagrams for topologies of Steiner minimal trees and minimal fillings for nonconvex four-pointed boundaries are constructed. Using this issue, the four-pointed Steiner subratio of the Euclidean plane is recieved. All configurations for which it is obtained are found.

Key words: Steiner minimal tree, minimal filling, Steiner subratio.

UDC: 514.77+519.176+515.165.7

Received: 20.05.2015