Integral bounds on curvature, elliptic estimates and rectifiability of singular sets

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K‐Stability and Kähler‐Einstein Metrics (2012, background): “11 The proof of (C4) uses the slicing argument in [11] (also see [8]) for proving that S2n 2 D ¿ in the case of smooth Kähler-Einstein metrics.”
Regularity of Kähler–Ricci flows on Fano manifolds (2013, background): “The estimates up to now combining with the segment inequality in next subsection are sufficient to generalize the regularization theory of Cheeger-Colding [8, 9, 10], Cheeger-Colding-Tian [11] and Cheeger [7] to manifolds satisfying (2.1) and (2.2).”
L2 curvature bounds on manifolds with bounded Ricci curvature (2016, background): “[8] Cheeger, Jeff, Integral bounds on curvature elliptic estimates and rectifiability of singular sets, Geom.”
Lower bounds on Ricci curvature and quantitative behavior of singular sets (2011, methodology): “19), strengthen the known bounds on the Hausdorff measure Hn−2p(S n−2p) which in particular is finite; see [4, 7].”