Geodesic
On sets containing a unit distance in every direction
Discrete analysis (2021) Cet article a éte moissonné depuis la source Scholastica

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We investigate the box dimensions of compact sets in $\mathbb{R}^2$ that contain a unit distance in every direction (such sets may have zero Hausdorff dimension). Among other results, we show that the lower box dimension must be at least $\frac{4}{7}$ and can be as low as $\frac{2}{3}$. This quantifies in a certain sense how far the unit circle is from being a difference set.
Publié le : 
@article{DAS_2021_a21,
     author = {Pablo Shmerkin and Han Yu},
     title = {On sets containing a unit distance in every direction},
     journal = {Discrete analysis},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2021_a21/}
}
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AU  - Pablo Shmerkin
AU  - Han Yu
TI  - On sets containing a unit distance in every direction
JO  - Discrete analysis
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/DAS_2021_a21/
LA  - en
ID  - DAS_2021_a21
ER  - 
%0 Journal Article
%A Pablo Shmerkin
%A Han Yu
%T On sets containing a unit distance in every direction
%J Discrete analysis
%D 2021
%U http://geodesic.mathdoc.fr/item/DAS_2021_a21/
%G en
%F DAS_2021_a21
Pablo Shmerkin; Han Yu. On sets containing a unit distance in every direction. Discrete analysis (2021). http://geodesic.mathdoc.fr/item/DAS_2021_a21/