2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186505The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invariant under the group of boost isometries. As an application, a proper star-surface is constructed.13 pages, comment added in section 2General Relativity and Quantum Cosmologytext