Branching solutions to one-dimensional variational problems - Ivanov, A. O., (Alexander O.) (World Scientific, 2001)
Includes bibliographical references (pages 323-329) and index
This study 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) it investigates 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