The standard double soap bubble in \(\mathbb{R}^ 2\) uniquely minimizes perimeter
Of course the circle is the least-perimeter way to enclose a region of prescribed area in the plane. This paper proves that a certain standard ``double bubble'' is the least-perimeter way to enclose and separate two regions of prescribed areas. The solution for three regions remains conjectural.
scientific article; zbMATH DE number 4216171