Branching Solutions to One-Dimensional Variational Problems

ISBN-13: 9789810240608 / Angielski / Twarda / 2001 / 364 str.

A. O. Ivanov; A. A. Tuzhilin

Opis

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.