Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds
Functional Analysis
2012-08-22 v1 Metric Geometry
Abstract
In this paper we show that embedded and compact manifolds have finite integral Menger curvature if and only if they are locally graphs of certain Sobolev-Slobodeckij spaces. Furthermore, we prove that for some intermediate energies of integral Menger type a similar characterization of objects with finite energy can be given.
Keywords
Cite
@article{arxiv.1110.4786,
title = {Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds},
author = {Simon Blatt and Sławomir Kolasiński},
journal= {arXiv preprint arXiv:1110.4786},
year = {2012}
}