2013
DOI: 10.1515/crelle-2013-0098
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Convergence of metrics under self-dual Weyl tensor and scalar curvature bounds

Abstract: We establish a C 1,α compactness theorem for the metrics with bounded self -dual Weyl tensor and Scalar curvature. The key step is to estimate the C 1,α harmonic radius, where we use the blow up analysis as in [Anderson90]. The result is motivated by, and may be applied to the Calabi flow on complex surfaces [Calabi82].

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