Quantitative comparisons of multiscale geometric properties

@article{Azzam2021QuantitativeCO,
  title={Quantitative comparisons of multiscale geometric properties},
  author={Jonas Azzam and Michele Villa},
  journal={Analysis \& PDE},
  year={2021}
}
We generalize some characterizations of uniformly rectifiable (UR) sets to sets whose Hausdorff content is lower regular (and in particular, do not need to be Ahlfors regular). For example, David and Semmes showed that, given an Ahlfors $d$-regular set $E$, if we consider the set $\mathscr{B}$ of surface cubes (in the sense of Christ and David) near which $E$ does not look approximately like a union of planes, then $E$ is UR if and only if $\mathscr{B}$ satisfies a Carleson packing condition… 

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