Convergence of metrics under self-dual Weyl tensor and scalar curvature bounds

Convergence of metrics under self-dual Weyl tensor and scalar curvature bounds

We establish a -compactness theorem for metrics with bounded self-dual Weyl tensor and scalar curvature. The main ingredient is the -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 flo...

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Veröffentlicht in:Journal für die reine und angewandte Mathematik 2016-01, Vol.2016 (710), p.57-76
1. Verfasser: Xu, Yiyan
Format: Artikel
Sprache:eng
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Zusammenfassung:We establish a -compactness theorem for metrics with bounded self-dual Weyl tensor and scalar curvature. The main ingredient is the -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.
ISSN:0075-4102
1435-5345
DOI:10.1515/crelle-2013-0098