Mathematicians Prove Major Conjecture on Singularity Formation in Evolving Surfaces
2025-04-06
Two mathematicians have proven Ilmanen's multiplicity-one conjecture, a long-standing problem in mathematics concerning the formation of singularities in mean curvature flow, a process that transforms general geometric objects into simpler, more symmetric ones. By cleverly decomposing surfaces into different regions and analyzing a 'separation function' between them, they showed that complicated singularities cannot occur; mean curvature flow almost always leads to two simple types: spheres shrinking to a point, or cylinders collapsing to a line. This breakthrough could have significant applications in geometry and topology and potentially simplify proofs of important problems, such as the Smale conjecture.
Tech
Topology