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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Jul 6, 1999
Published:
Jul 6, 1999

Related publications

inJournal
2002 Repository Open Access
Alexander O. Ivanov, Hông Vân Lê and Alexey A. Tuzhilin

Planar Manhattan local minimal and critical networks

In: European journal of combinatorics, 23 (2002) 8, pp. 949-967