The perimeter-minimizing enclosure of two areas in \(S^2\)
It is shown that the least-perimeter way to enclose and separate two prescribed areas in \(S^2\) is the standard double bubble. For given areas \(A_1,A_2>0\), with \(A_1+A_2<4\pi \), there exists a unique standard double bubble in the unit round sphere enclosing and separating regions of area \(A_1\) and \(A_2\).
scientific article; zbMATH DE number 1450289