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Integral curvature estimates and geodesic limits for stable abelian Higgs fields
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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BibTeX
@misc{badran2026integral,
title = {{Integral curvature estimates and geodesic limits for stable abelian Higgs fields}},
author = {Marco Badran and Marco A. M. Guaraco and Aria Halavati},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.21893},
eprint = {2609.21893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21893},
}
RIS
TY - UNPB
TI - Integral curvature estimates and geodesic limits for stable abelian Higgs fields
AU - Marco Badran
AU - Marco A. M. Guaraco
AU - Aria Halavati
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.21893
UR - https://arxiv.org/abs/2609.21893
AB - 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.
ER -