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arXiv · 2609.21893

Integral curvature estimates and geodesic limits for stable abelian Higgs fields

Marco Badran·Marco A. M. Guaraco·Aria Halavati
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Abstract

We prove that, on closed three-manifolds, the limit interface of a sequence of stable abelian Higgs critical points with uniformly bounded energy is a finite union of smooth closed immersed geodesics, possibly with multiplicity and self-intersections. This follows from an integral estimate for the diffuse curvature, derived from an integral bound on the discrepancy.

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Marco Badran, Marco A. M. Guaraco, Aria Halavati. 2026-09-18. Integral curvature estimates and geodesic limits for stable abelian Higgs fields. https://arxiv.org/abs/2609.21893

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