Extreme networks (Q5945243)

The paper gives an overview on the so-called extreme network theory. The origins of this theory are the classical Steiner problem, which asks to find a shortest network spanning a given finite set of points in the plane, and the one-dimensional variational calculus, which investigates extremals of variational functionals defined on a space of curves joining a pair of fixed points in an ambient space. As a common generalization of the two problems the paper discusses the structure of extreme networks in several spaces with a specific view to Riemannian manifolds, finite-dimensional real vector spaces and normalized spaces. A good collection of references is given.