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A Compactness Theorem for Yang-Mills Connections

Published online by Cambridge University Press:  20 November 2018

Xi Zhang
Xi Zhang*
Affiliation:
Department of Mathematics Zhejiang University Hangzhou, 310027 People’s Republic of China, e-mail: xizhang@zju.edu.cn
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Abstract

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In this paper, we consider Yang-Mills connections on a vector bundle $E$ over a compact Riemannian manifold $M$ of dimension $m\,>\,4$, and we show that any set of Yang-Mills connections with the uniformly bounded ${{L}^{\frac{m}{2}}}$-norm of curvature is compact in ${{C}^{\infty }}$ topology.

Keywords

58E2053C21Yang-Mills connectionvector bundlegauge transformation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 4 , 01 December 2004 , pp. 624 - 634
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Uhlenbeck, K. K., Removable singularities in Yang-Mills fields. Comm. Math. Phys. 83 (1982), 11–29.Google Scholar
[2] Uhlenbeck, K. K., Connections with Lp bounds on curvature. Comm. Math. Phys. 83 (1982), 31–42.Google Scholar
[3] Nakajima, H., Compactness of the moduli space of Yang-Mills connections in higher dimensions. J. Math. Soc. Japan 40 (1988), 383–392.Google Scholar
[4] Tian, G., Gauge theory and calibrated geometry. Ann.Math. 151 (2000), 193–208.Google Scholar
[5] Price, P., A monotonicity formula for Yang-Mills fields. Manuscripta Math. 43 (1983), 131–166.Google Scholar
[6] Sibner, L. M., The isolated point singularity problem for the coupled Yang-Mills eqaution in higher dimensions. Math. Ann. 271 (1985), 125–131.Google Scholar