Soap bubbles in ℝ2and in surfaces
Frank Morgan · Pacific Journal of Mathematics · 1994
We prove existence and regularity for "soap bubbles" in M 2 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.