2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167077We study the converse to the statement that instantons are minimizers of the Yang--Mills energy in four dimensions. We show that given an energy minimizing connection, A, the curvature of A takes values in a subbundle of the adjoint bundle which decomposes as a sum of instantons.16 pages; removed sections on duality for tori in dimensions greater than 4 and on G_2; references addedDifferential Geometry53C07text