Branching Solutions to One-Dimensional Variational Problems - Ivanov, Alexandr; Tuzhilin, Alexei Avgustinovich
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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.

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Produktbeschreibung
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.