New Proofs Probe Soap-Film Singularities

Mathematicians have made significant progress in understanding 'minimizing surfaces,' which are crucial in both math and physics. After decades of stagnation, a team led by Chodosh, along with Mantoulidis, Schulze, and Wang, demonstrated that in dimensions nine through eleven, smooth minimizing surfaces are the norm, resolving a long-standing problem. This breakthrough not only advances the study of higher-dimensional surfaces but also enhances the scope of related mathematical theorems and conjectures, potentially extending them to higher dimensions.