The structure of singularities in Π-minimizing networks in R2

Abstract

It is well known that length-minimizing networks in R2 consist of segments meeting only in threes. This paper considers uniformly convex norms Π more general than length. The first theorem says that for any such smooth Π, minimizing networks still meet only in threes. The second theorem shows that for some piecewise smooth Π, segments can meet in fours (although never in fives or more). © 1991 by Pacific Journal of Mathematics.