Falconer distance problem on Riemannian manifolds
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866909359295954944 |
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| author | Jian, Changbiao Liu, Bochen Xi, Yakun |
| author_facet | Jian, Changbiao Liu, Bochen Xi, Yakun |
| contents | We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)^d}{8d}.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01204 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Falconer distance problem on Riemannian manifolds Jian, Changbiao Liu, Bochen Xi, Yakun Classical Analysis and ODEs Analysis of PDEs We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)^d}{8d}.$$ |
| title | Falconer distance problem on Riemannian manifolds |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2309.01204 |