2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68874In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only singularities are neck pinches, and components which collapse to asymptotically round spheres.Differential GeometryAnalysis of PDEs53C44Singularity structure in mean curvature flow of mean convex setstext