The structure of singularities in Φ-minimizing networks in R²

Manuel Alfaro Garcia, Mark Conger and Kenneth Hodges

Vol. 149 (1991), No. 2, 201–210

DOI: 10.2140/pjm.1991.149.201

Abstract

It is well known that length-minimizing networks in R² consist of segments meeting only in threes. This paper considers uniformly convex norms Φ more general than length. The first theorem says that for any such smooth Φ, minimizing networks still meet only in threes. The second theorem shows that for some piecewise smooth Φ, segments can meet in fours (although never in fives or more).

Mathematical Subject Classification 2000

Primary: 90C35

Secondary: 49Q99

Milestones

Received: 1 October 1989

Revised: 30 May 1990

Published: 1 June 1991