2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166664We show existence and uniqueness for timelike minimal submanifolds in ambient Lorentz manifolds admitting a time function. The initial value formulation introduced and the conditions imposed on the initial data are given in purely geometric terms.109 pages, no figures, references updatedGeneral Relativity and Quantum Cosmologytext