Integral Menger curvature for sets of arbitrary dimension and codimension

Details Integral Menger curvature for sets of arbitrary dimension and codimension Integral Menger curvature for sets of arbitrary dimension and codimension

2010-11-09

arxiv.org/abs/1011.2008v5

Mathematics

Analysis of PDEs

Scientific paper

We propose a notion of integral Menger curvature for compact, $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies that the set is $C^{1,\alpha}$ embedded manifold with the H{\"o}lder norm and the size of maps depending only on the curvature. We develop the ideas introduced by Strzelecki and von der Mosel [Adv. Math. 226(2011)] and use a similar strategy to prove our results.

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