Branching Solutions to One-Dimensional Variational Problems
World Scientific Publishing Company | ISBN: 9810240600 | 2001-04 | PDF | 364 pages | 7 Mb
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.
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