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We obtain a local smoothing result for Riemannian manifolds with
bounded Ricci curvatures in dimension four. More precisely, given a
Riemannian metric with bounded Ricci curvature and small L^2-norm of
curvature on a metric ball, we can find a smooth metric with bounded
curvature which is C^1^,^@a-close to the original metric on a smaller ball
but still of definite size.
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