Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms

Gary Reid Lawlor and Frank Morgan

Vol. 166 (1994), No. 1, 55–83

DOI: 10.2140/pjm.1994.166.55

Abstract

In this paper we introduce a new method for proving area-minimization which we call “paired calibrations.” We begin with the simplest application, the cone over the tetrahedron, which appears in soap films. We then discuss immiscible fluid interfaces, crystal surfaces, and one-dimensional networks minimizing other norms.

Mathematical Subject Classification 2000

Primary: 58E12

Secondary: 49Q05

Milestones

Received: 27 May 1992

Accepted: 7 December 1992

Published: 1 November 1994