Geodesic
Exceptional set estimates for radial projections in R^n
Paige Bright1 ; Shengwen Gan2
1 Massachusetts Institute of Technology, Department of Mathematics
2 University of Wisconsin-Madison, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 631–661.

Voir la notice de l'article provenant de la source Journal.fi

  We prove two conjectures in this paper. The first conjecture is by Lund, Pham and Thu: Given a Borel set $A\subset \mathbb{R}^n$ such that $\dim A\in (k,k+1]$ for some $k\in\{1,\dots,n-1\}$. For $0, we have   $\text{dim}(\{y\in \mathbb{R}^n \setminus A\mid \text{dim} (\pi_y(A)) < s\})\leq \max\{k+s -\dim A,0\}.$   The second conjecture is by Liu: Given a Borel set $A\subset \mathbb{R}^n$, then $\text{dim} (\{x\in \mathbb{R}^n \setminus A \mid \text{dim}(\pi_x(A))<\text{dim} A\}) \leq \lceil \text{dim} A\rceil.$  
DOI : 10.54330/afm.152156
Keywords: Radial projection, exceptional estimate

Paige Bright 1 ; Shengwen Gan 2

1 Massachusetts Institute of Technology, Department of Mathematics
2 University of Wisconsin-Madison, Department of Mathematics 
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Paige Bright; Shengwen Gan. Exceptional set estimates for radial projections in R^n. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 631–661. doi : 10.54330/afm.152156. http://geodesic.mathdoc.fr/articles/10.54330/afm.152156/

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