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- W4205262594 abstract "Given a k-point configuration $$xin ({mathbb {R}}^d)^k$$ (where $$kge d$$ ), we consider the $$left( {begin{array}{c}k dend{array}}right) $$ -vector of volumes determined by choosing any d points of x. We prove that a compact set $$Esubset {mathbb {R}}^d$$ determines a positive measure of such volume types if the Hausdorff dimension of E is greater than $$d-frac{d-1}{2k-d}$$ . This generalizes results of Greenleaf et al. (Forum Math 27(1):635–646, 2015) and (On k-point configuration sets with nonempty interior, https://arxiv.org/abs/2005.10796 , 2020) and the McDonald (in: Proceedings of the AMS, https://arxiv.org/abs/2008.13720 )." @default.
- W4205262594 created "2022-01-25" @default.
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- W4205262594 date "2021-12-09" @default.
- W4205262594 modified "2023-09-27" @default.
- W4205262594 title "Volumes Spanned by k-Point Configurations in $${mathbb {R}}^d$$" @default.
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- W4205262594 doi "https://doi.org/10.1007/s12220-021-00763-5" @default.
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