Soap bubbles in R2 and in surfaces

Abstract

We prove existence and regularity for "soap bubbles" in M2 and in surfaces, i.e., the least-perimeter way to enclose and separate regions of prescribed area. They consist of constant-curvature arcs meeting in threes at 120 degrees. If one prescribes the combinatorial type too, then the arcs may bump up against each other. © 1994 by Pacific Journal of Mathematics.