, Volume 141, Issue 1-2, pp 125-147,
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Minimal Hölder regularity implying finiteness of integral Menger curvature

Abstract

We study two kinds of integral Menger-type curvatures. We find a threshold value of α 0, a Hölder exponent, such that for all αα 0 embedded C 1,α manifolds have finite curvature. We also give an example of a ${C^{1,\alpha_0}}$ injective curve and higher dimensional embedded manifolds with unbounded curvature.