• Corpus ID: 245218865

On the distance sets spanned by sets of dimension $d/2$ in $\mathbb{R}^d$

@inproceedings{Shmerkin2021OnTD,
  title={On the distance sets spanned by sets of dimension \$d/2\$ in \$\mathbb\{R\}^d\$},
  author={Pablo Shmerkin and Hong Wang},
  year={2021}
}
We establish the dimension version of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In dimensions d = 2 or 3, we obtain the first explicit estimates for the dimensions of distance sets of general Borel sets of dimension d/2; for example, we show that the set of distances spanned by a planar Borel set of Hausdorff dimension 1 has Hausdorff dimension at least ( √ 5 − 1)/2 ≈ 0.618. In higher… 
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4 Citations
Background Citations
3
Methods Citations
2

4 Citations

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Discretized sum-product type problems: Energy variants and Applications

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