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# A Compactness Theorem for Yang-Mills Connections

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Published:2004-12-01
Printed: Dec 2004
• Xi Zhang
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## Abstract

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: Yang-Mills connection, vector bundle, gauge transformation
 MSC Classifications: 58E20 - Harmonic maps [See also 53C43], etc. 53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

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