2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67764We obtain estimates on both size and dimensions of the singular set at the first blow-up time of the mean curvature flow of hypersurfaces whose initial data is $σ_k$-convex.to appear in Houston Journal of MathematicsDifferential Geometry53C, 58JOn the Mean Curvature Flow for $σ_k$-Convex Hypersurfacestext