Scalar curvature lower bounds are preserved under weak limits of smooth closed 3-manifolds through μ-bubble comparisons when volumes and Lipschitz constants converge appropriately.
Ricci curvature for metric-measure spaces via optimal transport.Annals of Mathe- matics, pages 903–991, 2009
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Scalar curvature under weak limits of manifolds
Scalar curvature lower bounds are preserved under weak limits of smooth closed 3-manifolds through μ-bubble comparisons when volumes and Lipschitz constants converge appropriately.