Abstract
Abstract We establish a C 1,α-compactness theorem for metrics with bounded self-dual Weyl tensor and scalar curvature. The main ingredient is the C 1,α-harmonic radius estimate, where a blow up analysis as in [Invent. Math. 102 (1990), 429–445] is used. Our result is motivated by, and may be applied to, the Calabi flow on complex surfaces.
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