Estimating discrete curvatures in terms of beta numbers

Published 3 May 2016 in math.CA | (1605.00939v1)

Abstract: For an arbitrary Radon measure $\mu$ we estimate the integrated discrete curvature of $\mu$ 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].

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Sławomir Kolasiński

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