Branching Solutions To One-dimensional Variational Problems

ISBN: 9789810240608 出版年：2001 页码：365 Alexandr Ivanov Alexei Avgustinovich Tuzhilin World Scientific Publishing Company

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.