This book focuses on the classic Steiner Problem and illustrates how results of the problem's
development have generated the Theory of Minimal Networks, that is systems of" rubber" …

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 …

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 …

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 …

We study the existence of minimal networks in the unit sphere S d and the unit ball B d of R d
endowed with Riemannian metrics close to the standard ones. We employ a finite …

AO Ivanov, “The geometry of plane locally minimal binary trees”, Mat. Sb., 186:9 (1995), 45–76;
Sb. Math., 186:9 (1995), 1271–1301 Sbornik: Mathematics RUS ENG JOURNALS PEOPLE …

We are interested in generalizing the classical Cauchy Rigidity Theorem and the
Aleksandrov's Existence Theorem for convex polyhedra and the sphere to the closed …

In this paper we study the structure of the set of all locally minimal plane networks with a
fixed topology and a fixed boundary. It is shown that if this set is non-empty, then it is a …

This paper is supposed to be a review on the new branch of mathematics–extreme networks
theory that appeared at the crossroad of differential geometry, variational calculus and …

В отличие от евклидова случая, на гладких римановых многообразиях минимальные
деревья Штейнера для конкретных границ практически не известны. В работе получен …