2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65216This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key is to understand the structure of an embedded minimal disk in a ball in $\RR^3$. This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see [CM15] for discussion of the local case and [CM13], [CM14] where we have surveyed our results about embedded minimal disks.Figures added to existing preprintAnalysis of PDEsDifferential Geometrytext