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A Compactness Theorem for Yang-Mills Connections |
Canad. Math. Bull. 47(2004), 624-634
Published:2004-12-01
Printed: Dec 2004
Printed: Dec 2004
- Xi Zhang
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] |