The aim of this note is to clear some background information and references to readers
interested in understanding the current status of the Gilbert–Pollak Conjecture, in particular …

Abstract Minimal Networks Theory is a branch of mathematics that goes back to 17th century
and unites ideas and methods of metric, differential, and combinatorial geometry and …

We offer evidence in the disproof of the continuity of the length of minimum inner spanning
trees with respect to a parameter vector having a zero component. The continuity property is …

1. Introduction. Let M be a complete Riemannian manifold without boundary. Let P be a finite
set of points in M. A shortest network interconnecting P is called a Steiner minimum tree …

The following result is proved: there exists an open dense subset of such that each
(regarded as an enumerated subset of the standard Euclidean plane) is spanned by a …

Let D be a compact polygonal Alexandrov surface with curvature bounded below by κ. We
study the minimum network problem of interconnecting the vertices of the boundary …

In this paper, we study the weighted Fermat-Frechet problem for a $\frac {N (N+ 1)}{2}-$
tuple of positive real numbers determining $ N $-simplexes in the $ N $ dimensional $ K …

STEINER SUBRATIO OF RIEMANNIAN MANIFOLDS EI Stepanova UDC 514.74; 515.124.4;
519.176 Page 1 Journal of Mathematical Sciences, Vol. 276, No. 3, October, 2023 STEINER …

Abstract The Steiner–Gromov ratio of a metric space X characterizes the ratio of the minimal
filling weight to the minimal spanning tree length for a finite subset of X. It is proved that the …

In the paper minimal fillings of finite metric spaces are investigated. This object appeared as
a generalization of the concepts of a shortest tree and a minimal filling in the sense of …