Isolated Singularities of Yang-Mills-Higgs fields on surfaces

Bo Chen; Chong Song

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arXiv · 1907.07092

Isolated Singularities of Yang-Mills-Higgs fields on surfaces

Bo Chen·Chong Song

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Abstract

We study isolated singularities of two dimensional Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a compact connected Lie group. In general the singularity can not be removed due to possibly non-vanishing limit holonomy around the singular points. We establish a sharp asymptotic decay estimate of the Yang-Mills-Higgs field near a singular point, where the decay rate is precisely determined by the limit holonomy. Our result can be viewed as a generalization of the classical removable singularity theorem of two dimensional harmonic maps.

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BibTeX RIS

Bo Chen, Chong Song. 2019-07-16. Isolated Singularities of Yang-Mills-Higgs fields on surfaces. https://arxiv.org/abs/1907.07092

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