Integral Menger curvature for sets of arbitrary dimension and codimension
Kolasiński, Sławomir
arXiv, 1011.2008 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2010-11-09
Classification:  Mathematics - Analysis of PDEs,  Mathematics - Metric Geometry,  49Q15, 49Q20, 28A75 
@article{1011.2008,
     author = {Kolasi\'nski, S\l awomir},
     title = {Integral Menger curvature for sets of arbitrary dimension and
  codimension},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1011.2008}
}

Kolasiński, Sławomir. Integral Menger curvature for sets of arbitrary dimension and
  codimension. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1011.2008/