Uniqueness conjecture for mean curvature flow of embedded two-spheres

Consider mean curvature flows starting from embedded two-spheres and allowing singularities. Uniqueness conjecture for mean curvature flow of embedded two-spheres. The mean curvature flow of embedded two-spheres through singularities is unique. Uniqueness would give a well-posed continuation through singularities and has applications to geometric and topological problems. The paper proves the conjecture conditional on a special case of the multiplicity-one conjecture; the remaining multiplicity-one issue is not resolved in the source.