Title: Proving area minimization by directed slicing

Authors: Gary Lawlor

Issue: Volume 47 (1998), Issue 4, 1547-1592

Abstract: We set forth a highly geometric, versatile method for proving area minimization. It provides a powerful way of obtaining new results, particularly for unorientable surfaces, size-minimizing surfaces, highly singular surfaces, and unions of minimal surfaces. This is the foundational paper for this method. We will lay out the basics, illustrate with some examples, and in Theorems 5.13 through 5.15 prove new minimization results. These are that certain pairs of $k$-planes are minimizing among nonoriented surfaces, that certain pairs are size-minimizing, and that certain surfaces with 120-degree triple junctions along large singular sets are size-minimizing.