The paper is devoted to a new branch in the theory of one-dimensional variational problems
with branching extremals, the investigation of one-dimensional minimal fillings introduced by …

Статья посвящена новому направлению в теории одномерных вариаци онных задач с
разветвленными экстремалями-исследованию одномерных минимальных заполнений …

Пусть (X, ρ)–метрическое пространство, G=(V, E)–связный граф со множеством вершин
V и множеством ребер E. Отображение Γ: V→ X называется сетью в X …

It is proved that a real Banach space realizes minimal fillings for all its finite subsets (a
shortest network spanning a fixed finite subset always exists and has the minimum possible …

The aim in this graduate level text is to outline the key mathematical concepts that underpin
these important questions in applied mathematics. These concepts involve discrete …

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 …

In the present paper we consider local minimal and extremal networks in normed spaces. It
is well known that in the case of the Euclidean space these two classes coincide and the …

A Continuity Criterion for Steiner-Type Ratios in the Gromov–Hausdorff Space Page 1 ISSN
0001-4346, Mathematical Notes, 2014, Vol. 96, No. 1, pp. 130–139. © Pleiades Publishing …

We introduce the notion of animmersed polygon', which naturally extends the notion of an
ordinary planar polygon bounded by a closed (embedded) polygonal arc to the case when …

In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries
on Riemannian manifolds are known. A result describing the types of Steiner minimal trees …