2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105776We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical insterest, such as dynamical horizons.28 pages. This is a major rework of the previous version. It extends the curvature estimates to no longer require global area bounds. In addition some mistakes were correctedGeneral Relativity and Quantum CosmologyDifferential Geometrytext