Estimating discrete curvatures in terms of beta numbers
Classical Analysis and ODEs
2016-05-04 v1
Abstract
For an arbitrary Radon measure we estimate the integrated discrete curvature of in terms of its centred variant of Jones' beta numbers. We farther relate integrals of centred and non-centred beta numbers. As a corollary, employing the recent result of Tolsa [Calc. Var. PDE, 2015], we obtain a partial converse of the theorem of Meurer [arXiv:1510.04523].
Keywords
Cite
@article{arxiv.1605.00939,
title = {Estimating discrete curvatures in terms of beta numbers},
author = {Sławomir Kolasiński},
journal= {arXiv preprint arXiv:1605.00939},
year = {2016}
}