# Sufficient Condition for Rectifiability Involving Wasserstein Distance $$W_2$$

@article{Dbrowski2019SufficientCF, title={Sufficient Condition for Rectifiability Involving Wasserstein Distance \$\$W\_2\$\$}, author={Damian Dąbrowski}, journal={arXiv: Classical Analysis and ODEs}, year={2019} }

A Radon measure $\mu$ is $n$-rectifiable if it is absolutely continuous with respect to $\mathcal{H}^n$ and $\mu$-almost all of $\text{supp}\,\mu$ can be covered by Lipschitz images of $\mathbb{R}^n$. In this paper we give two sufficient conditions for rectifiability, both in terms of square functions of flatness-quantifying coefficients. The first condition involves the so-called $\alpha$ and $\beta_2$ numbers. The second one involves $\alpha_2$ numbers -- coefficients quantifying flatness via… Expand

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Necessary Condition for Rectifiability Involving Wasserstein Distance W2

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A Radon measure $\mu$ is $n$-rectifiable if $\mu\ll\mathcal{H}^n$ and $\mu$-almost all of $\text{supp}\,\mu$ can be covered by Lipschitz images of $\mathbb{R}^n$. In this paper we give a necessary… Expand

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