Improved bounds for radial projections in the plane
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914023028555776 |
|---|---|
| author | Csornyei, Marianna Stull, D. M. |
| author_facet | Csornyei, Marianna Stull, D. M. |
| contents | We improve the best known lower bound for the dimension of radial projections of sets in the plane. We show that if $X,Y$ are Borel sets in $\R^2$, $X$ is not contained in any line and $\dim_H(X)>0$, then
$$\sup\limits_{x\in X} \dim_H(π_x Y) \geq \min\left\{(\dim_H(Y) + \dim_H(X))/2, \dim_H(Y), 1\right\},$$ where $π_x Y$ is the radial projection of the set $Y$ from the point $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved bounds for radial projections in the plane Csornyei, Marianna Stull, D. M. Classical Analysis and ODEs We improve the best known lower bound for the dimension of radial projections of sets in the plane. We show that if $X,Y$ are Borel sets in $\R^2$, $X$ is not contained in any line and $\dim_H(X)>0$, then $$\sup\limits_{x\in X} \dim_H(π_x Y) \geq \min\left\{(\dim_H(Y) + \dim_H(X))/2, \dim_H(Y), 1\right\},$$ where $π_x Y$ is the radial projection of the set $Y$ from the point $x$. |
| title | Improved bounds for radial projections in the plane |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.18228 |