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

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. © 1994 by Pacific Journal of Mathematics.