Integral Menger curvature for sets of arbitrary dimension and codimension
Analysis of PDEs
2015-03-17 v6 Metric Geometry
Abstract
We propose a notion of integral Menger curvature for compact, -dimensional sets in -dimensional Euclidean space and prove that finiteness of this quantity implies that the set is 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.
Keywords
Cite
@article{arxiv.1011.2008,
title = {Integral Menger curvature for sets of arbitrary dimension and codimension},
author = {Sławomir Kolasiński},
journal= {arXiv preprint arXiv:1011.2008},
year = {2015}
}
Comments
This dissertation is not going to be published. The article "Geometric Sobolev-like embedding using high-dimensional Menger-like curvature" [arXiv:1205.4112] obsoletes my thesis. For any further reference one should use [arXiv:1205.4112] or its published version