The paper establishes non-trivial dimensional thresholds for volume vectors determined by hypergraphs of simplices via a Jacobian method leveraging distance results and a refinement for planar triangles, improving prior bounds.
New improvement to falconer distance set problem in higher dimensions
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
years
2026 4verdicts
UNVERDICTED 4representative citing papers
Delsarte LP on the quadratic-form association scheme proves that |E| ≳ q^{n/2 + 1/3} forces |Δ_Q(E)| ≫ q for even n and large odd prime-power q.
Borel sets with Fourier dimension at least 2 have distance sets of full Hausdorff dimension in any ambient dimension d, and sets with Fourier spectrum at least d/4 + 1 at theta = 1/2 also achieve this even when their Fourier dimension is zero provided d is at least 4.
Under dim_H E >1, dim_H E + dim_H F >2 and F regular (equal Hausdorff and packing dimensions), there exists y in F such that the pinned distance set Δ_y(E) has positive Lebesgue measure.
citing papers explorer
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On volume vectors determined by hypergraphs in thin subsets of Euclidean space
The paper establishes non-trivial dimensional thresholds for volume vectors determined by hypergraphs of simplices via a Jacobian method leveraging distance results and a refinement for planar triangles, improving prior bounds.
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A Delsarte Linear Programming Approach to the Erd\H{o}s--Falconer Distance Problem over Finite Fields
Delsarte LP on the quadratic-form association scheme proves that |E| ≳ q^{n/2 + 1/3} forces |Δ_Q(E)| ≫ q for even n and large odd prime-power q.
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On Fourier decay and the distance set problem
Borel sets with Fourier dimension at least 2 have distance sets of full Hausdorff dimension in any ambient dimension d, and sets with Fourier spectrum at least d/4 + 1 at theta = 1/2 also achieve this even when their Fourier dimension is zero provided d is at least 4.
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Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates
Under dim_H E >1, dim_H E + dim_H F >2 and F regular (equal Hausdorff and packing dimensions), there exists y in F such that the pinned distance set Δ_y(E) has positive Lebesgue measure.