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Acta Applicandae Mathematica

, Volume 66, Issue 3, pp 251–318 | Cite as

Extreme Networks

  • Alexandr O. Ivanov
  • Alexey A. Tuzhilin
Article

Abstract

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 discrete mathematics. One of the starting points of the theory is the geometrical approach to the Steiner problem. The authors have selected the most impressive results of the theory demonstrating a new approach, new effects, and new constructions appearing in this context. One of the main aims of the paper is to attract the attention of the specialist from similar fields to this new and rapidly developing theory.

extreme networks geometrical variational problems one-dimensional variational problems branching geodesics branching solutions Steiner problem Steiner ratio 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Alexandr O. Ivanov
    • 1
  • Alexey A. Tuzhilin
    • 1
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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