Convergence of Einstein Yang-Mills systems
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Abstract:
In this paper, we prove a convergence theorem for sequences of Einstein Yang-Mills systems on $U(1)$-bundles over closed $n$-manifolds with some bounds for volumes, diameters, $L^{2}$-norms of bundle curvatures, and $L^{\frac {n}{2}}$-norms of curvature tensors. This result is a generalization of earlier compactness theorems for Einstein manifolds.References
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Additional Information
- Hongliang Shao
- Affiliation: Department of Mathematics, Capital Normal University, Beijing, People’s Republic of China 100048
- Address at time of publication: College of Mathematics and Statistics, Chongqing University, 55, Daxuecheng South Road, Shapingba, Chongqing, People’s Republic of China 401331
- Email: hongliangshao@foxmail.com
- Received by editor(s): January 2, 2012
- Received by editor(s) in revised form: April 16, 2012
- Published electronically: December 10, 2013
- Communicated by: Lei Ni
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 969-979
- MSC (2010): Primary 53C21, 53C23
- DOI: https://doi.org/10.1090/S0002-9939-2013-11817-4
- MathSciNet review: 3148531