An improved result for Falconer’s distance set problem in even dimensions
نویسندگان
چکیده
We show that if compact set $$E\subset \mathbb {R}^d$$ has Hausdorff dimension larger than $$\frac{d}{2}+\frac{1}{4}$$ , where $$d\ge 4$$ is an even integer, then the distance of E positive Lebesgue measure. This improves previously best known result towards Falconer’s conjecture in dimensions.
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2021
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-021-02170-1