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A Compactness Theorem for Yang-Mills Connections

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

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