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Connections withL P bounds on curvature

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We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inR n when the integralL n/2 field norm is sufficiently small. We then are able to prove a weak compactness theorem for fields on compact manifolds withL p integral norms bounded,p>n/2.

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Communicated by S.-T. Yau

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Uhlenbeck, K.K. Connections withL P bounds on curvature. Commun.Math. Phys. 83, 31–42 (1982).

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