Abstract
We prove that for any compact set E ⊂ R2, dimH(E) > 1, there exists x ∈ E such that the Hausdorff dimension of the pinned distance set (Equation Presented) is no less than min {4 3 dimH(E) - 2 3 , 1}. This answers a question recently raised by Guth, Iosevich, Ou, and Wang, as well as improves results of Keleti and Shmerkin.
| Original language | English |
|---|---|
| Pages (from-to) | 333-341 |
| Number of pages | 9 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 148 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2020 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019 American Mathematical Society.
Funding
Received by the editors May 13, 2019. 2010 Mathematics Subject Classification. Primary 28A75; Secondary 42B20. Key words and phrases. Hausdorff dimension, Falconer distance conjecture, pinned distances. The author was supported by the grant CUHK24300915 from the Hong Kong Research Grant Council.
| Funders | Funder number |
|---|---|
| Hong Kong Arts Development Council |
Keywords
- Falconer distance conjecture
- Hausdorff dimension
- Pinned distances