Branching solutions to one-dimensional variational problems

Alexandr O. Ivanov, A. A. Tuzhilin9810240600, 9789810240608, 9789812810717

This book deals with the new class of one-dimensional variational problems – the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.