Clusters with multiplicities in ℝ²

Frank Morgan

Vol. 221 (2005), No. 1, 123–146

DOI: 10.2140/pjm.2005.221.123

Abstract

Perimeter-minimizing planar double soap bubbles in which regions are allowed to overlap with multiplicities meet in fours, fives, and sixes as well as threes. We further provide certain generalizations to immiscible fluids and higher dimensions, and an associated theory of calibrations. We work in the category of flat chains with coefficients in a normed group.

Keywords

clusters with multiplicities, soap bubbles, immiscible fluids, paired calibrations, flat chains with coefficients in a normed group

Mathematical Subject Classification 2000

Primary: 49Q20

Milestones

Received: 2 January 2002

Revised: 22 July 2002

Published: 1 September 2005