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Falconer distance problem on Riemannian manifolds
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math.CAmath.AP
keywords
distancefracriemannianboreldimensionalfalconerfrac14lebesgue
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abstract
We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)^d}{8d}.$$
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