Manuscripta Mathematica

, Volume 141, Issue 1–2, pp 125–147

Minimal Hölder regularity implying finiteness of integral Menger curvature

Open Access

DOI: 10.1007/s00229-012-0565-y

Cite this article as:
Kolasiński, S. & Szumańska, M. manuscripta math. (2013) 141: 125. doi:10.1007/s00229-012-0565-y


We study two kinds of integral Menger-type curvatures. We find a threshold value of α0, a Hölder exponent, such that for all αα0 embedded C1,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.

Mathematics Subject Classification (1991)

Primary: 49Q10 Secondary: 28A75 49Q20 49Q15 

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarsawPoland

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