Branched Geodesics: Geometrical Theory of Local Minimal Networks

Author: Ivanov, A.
Tuzhilin, A. A.
The book is devoted to investigation of branched extremals of various one-dimensional variational functionals of the length functional type. These extremals have the structure of graphs mapped into Riemannian manifolds. The edges of them are geodesics meeting at the vertices in a way depending on the functional. Such network appeared first as solutions of the well-known Steiner Problem. These extremals turn to be important for various applications such as transportation problem, chip design, extrapolation of polygenetic trees, etc. The book presents as the modern state of the minimal networks theory as the review on classical results.