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MiS Preprint
46/1999
Planar Manhattan local minimal and critical networks
Alexandr O. Ivanov, Hông Vân Lê and Alexey A. Tuzhilin
Abstract
The present work is devoted to the investigation of branching extremals, i.e., extremal networks, of the Manhattan length functional. Recall that the Manhattan length of a straight segment in Rn is defined as the sum of the lengths of the segment projections to the Cartesian coordinate axis.
It turns out that in the case of Manhattan length functional the class of local minimal networks is wider than the one of critical networks. The main aim of the present work is to describe the difference between these classes.