Geodesic
Visible parts and slices of Ahlfors regular sets
Discrete analysis (2024) Cet article a éte moissonné depuis la source Scholastica

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We show that for any compact set $E\subset\mathbb{R}^d$ the visible part of $E$ has Hausdorff dimension at most $d-1/6$ for almost every direction. This improves recent estimates of Orponen and Matheus. If $E$ is $s$-Ahlfors regular, where $s>d-1$, we prove a much better estimate. In that case for almost every direction the Hausdorff dimension of the visible part is at most $s - α(s-d+1),$ where $α>0.183$ is absolute. The estimate is new even for self-similar sets satisfying the open set condition. Along the way, we prove a refinement of the Marstrand's slicing theorem for Ahlfors regular sets.
Publié le : 
@article{DAS_2024_a4,
     author = {Damian D\k{a}browski},
     title = {Visible parts and slices of {Ahlfors} regular sets},
     journal = {Discrete analysis},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2024_a4/}
}
TY  - JOUR
AU  - Damian Dąbrowski
TI  - Visible parts and slices of Ahlfors regular sets
JO  - Discrete analysis
PY  - 2024
UR  - http://geodesic.mathdoc.fr/item/DAS_2024_a4/
LA  - en
ID  - DAS_2024_a4
ER  - 
%0 Journal Article
%A Damian Dąbrowski
%T Visible parts and slices of Ahlfors regular sets
%J Discrete analysis
%D 2024
%U http://geodesic.mathdoc.fr/item/DAS_2024_a4/
%G en
%F DAS_2024_a4
Damian Dąbrowski. Visible parts and slices of Ahlfors regular sets. Discrete analysis (2024). http://geodesic.mathdoc.fr/item/DAS_2024_a4/