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Convergence of Einstein Yang-Mills systems


Author: Hongliang Shao
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
Published electronically: December 10, 2013
MathSciNet review: 3148531
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2013-11817-4
Keywords: Einstein Yang-Mills system, Gromov-Hausdorff convergence
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
Article copyright: © Copyright 2013 American Mathematical Society