Manuscripta Mathematica

, Volume 141, Issue 1, pp 125–147

Minimal Hölder regularity implying finiteness of integral Menger curvature

Authors

    • Institute of MathematicsUniversity of Warsaw
  • Marta Szumańska
    • Institute of MathematicsUniversity of Warsaw
Open AccessArticle

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

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.

Mathematics Subject Classification (1991)

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

Copyright information

© The Author(s) 2012