Abstract
Two examples are given of a sequence on a compactd-dimensional manifold (d ≥ 3) in a fixed conformal class satisfying a uniformL (d/2) bound on curvature and a bound on volume which are not compact in aC 0 topology. This shows that the curvature assumption of recent compactness results for conformal metrics is sharp.
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References
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Chang’s research supported in part by an NSF Grant. Gursky’s research supported in part by an NSF Postdoctoral Fellowship. The first and second authors gratefully acknowledge support from the Institute for Advanced Study, Princeton.
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Chang, S.Y.A., Gursky, M. & Wolff, T. Lack of compactness in conformal metrics withL d/2 curvature. J Geom Anal 4, 143–153 (1994). https://doi.org/10.1007/BF02921543
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DOI: https://doi.org/10.1007/BF02921543