Two quantitative definitions of α-regularity for Riemannian surfaces, one based on curvature and one on local metric coefficients, are shown to be equivalent up to constants depending on α.
T., Convergence and rigidity of manifolds under Ricci curvature bounds
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A quantitative approach to the regularity of a Riemannian surface
Two quantitative definitions of α-regularity for Riemannian surfaces, one based on curvature and one on local metric coefficients, are shown to be equivalent up to constants depending on α.