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Estimating discrete curvatures in terms of beta numbers

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Kolasinski,  Slawomir
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1605.00939.pdf
(Preprint), 376KB

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Citation

Kolasinski, S. (in preparation). Estimating discrete curvatures in terms of beta numbers.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-7188-9
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].