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arXiv · 1403.0780

Convergence of Yang-Mills-Higgs fields

Chong Song
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Abstract

In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We show that away from the nodes, the YMH fields converges, up to gauge, to a smooth YMH field modulo finitely many harmonic spheres, while near the nodes where the conformal structure degenerates, the YMH fields converges to a pair consisting of a flat connection and a twisted geodesic (with potential) after finitely many times of blowing-up's. In particular, we prove a generalized energy identity and give a refined analysis of the neck.

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Chong Song. 2014-03-04. Convergence of Yang-Mills-Higgs fields. https://arxiv.org/abs/1403.0780

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