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Nonabelian Higgs fields from minimal submanifolds
Abstract
We construct 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 b1(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 SU(2) Yang--Mills--Higgs fields.
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BibTeX
@misc{badran2026nonabelian,
title = {{Nonabelian Higgs fields from minimal submanifolds}},
author = {Marco Badran},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35837},
eprint = {2610.35837},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35837},
}
RIS
TY - UNPB
TI - Nonabelian Higgs fields from minimal submanifolds
AU - Marco Badran
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35837
UR - https://arxiv.org/abs/2610.35837
AB - We construct 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 SU(2) Yang--Mills--Higgs fields.
ER -