PreprintCC BY 4.0arXiv
Nonclosure of stationary Yang-Mills connections under weak convergence
Abstract
We construct a sequence of stationary weak Yang-Mills connections on the trivial vector bundle B5×ℝ15 with structure group SO(15) whose weak limit is a nonstationary weak Yang-Mills connection. Motivated by the stationarity question arising in Tian's work on Yang-Mills compactness, our result establishes the failure of weak closure for stationary weak Yang-Mills connections with an isolated singularity. It also provides a Yang-Mills analogue of the phenomenon exhibited by Ding, Li and Li for harmonic maps.
Related
- Decay estimates for Yang-Mills connections and Yang-Mills-Higgs pairs in higher dimensions
- Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory
- Algebraic limits of Hermitian-Yang-Mills connections on Kähler surfaces
- Non-Hermitian Yang--Mills Connections with Vanishing Chern Classes
- Compactness of Cone Yang-Mills Connections
BibTeX
@misc{han2026nonclosure,
title = {{Nonclosure of stationary Yang-Mills connections under weak convergence}},
author = {Xiaoli Han and Jiayu Li and Yang Wen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23338},
eprint = {2609.23338},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23338},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonclosure of stationary Yang-Mills connections under weak convergence
AU - Xiaoli Han
AU - Jiayu Li
AU - Yang Wen
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23338
UR - https://arxiv.org/abs/2609.23338
AB - We construct a sequence of stationary weak Yang-Mills connections on the trivial vector bundle B^5×ℝ^15 with structure group SO(15) whose weak limit is a nonstationary weak Yang-Mills connection. Motivated by the stationarity question arising in Tian's work on Yang-Mills compactness, our result establishes the failure of weak closure for stationary weak Yang-Mills connections with an isolated singularity. It also provides a Yang-Mills analogue of the phenomenon exhibited by Ding, Li and Li for harmonic maps.
ER -