Nonabelian Higgs fields from minimal submanifolds

We construct $\mathrm{SU}(2)$ Yang-Mills-Higgs fields on a broad class of noncompact Riemannian manifolds, concentrating in the large-mass limit along prescribed nondegenerate minimal submanifolds of codimension three. The solutions have uniformly bounded rescaled energy. On closed manifolds with $b_1(M)=0$, adding a suitably scaled Higgs potential gives an analogous concentration result. Our construction completes one direction of the correspondence proposed by Parise, Pigati and Stern, realising prescribed minimal submanifolds of codimension three as concentration sets of $\mathrm{SU}(2)$ Yang--Mills--Higgs fields.