We present a review on a new branch of one-dimensional geometrical optimization problem,
the minimal fillings theory. This theory is connected closely with generalized Steiner problem …

Fermat–Steiner problem consists in finding all points in a metric space Y such that the sum
of distances from each of them to the points from some fixed finite subset A of Y is minimal …

New necessary conditions for the nonlinear stability of branched tree-like structures
composed of elastic rods are presented. The conditions, which are found by examining the …

We find the equations of the two interior nodes (weighted Fermat–Torricelli points) with
respect to the weighted Steiner problem for four points determining a tetrahedron in R 3 …

We have selected problems that may not yet be well known, but have the potential to push
the research in interesting directions. In particular, we state problems that do not require …

The Steiner ratio characterizes the greatest possible deviation of the length of a minimal
spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the …

The Fermat-Steiner problem consists in finding all points in a metric space X at which the
sum of the distances to fixed points A1,..., An of X attains its minimum value. This problem is …

Structures featuring rod-like bodies connected in a branched ensemble are ubiquitous. They
appear in antennae, replicating DNA strands, and, most visibly, in the plant kingdom. In spite …

We study branching extremals of length functionals on normed spaces. This is a natural
generalization of the Steiner problem in normed spaces. We obtain criteria for a network to …

This is a basic text on the mathematical theory for optimal control problems governed by
ODEs in the sense that it addresses the most basic and pertinent questions in this field of …