Asymptotically optimally doubling measures and Reifenberg flat sets with vanishing constant

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Tangent-point self-avoidance energies for curves (2010, background): “2Let us remark that for an m-dimensional set Σ⊂Rn that is Reifenberg flat with vanishing constant uniform estimates of β -numbers imply that Σ is a C1,κ -manifold, see David, Kenig and Toro [9] and Preiss, Tolsa and Toro [17].”
Gradient estimates in Orlicz space for nonlinear elliptic equations (2008, background): “For a further discussion of Reifenberg flat domains we refer to [4,6,9,14,15,23].”
Integral Menger curvature for surfaces (2009, background): “The proof is presented in Section 5; it is self-contained and independent of [6] and [26].”
Parabolic Equations in Reifenberg Domains (2005, methodology): “, [7, 13, 14, 20, 23–26, 33]).”