, Volume 141, Issue 1-2, pp 125-147,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 28 Jun 2012

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.