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
$\text{dim} (\{x\in \mathbb{R}^n \setminus A \mid \text{dim}(\pi_x(A))<\text{dim} A\}) \leq \lceil \text{dim} A\rceil.$
1
Massachusetts Institute of Technology, Department of Mathematics
2
University of Wisconsin-Madison, Department of Mathematics
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
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title = {Exceptional set estimates for radial projections in {R^n}},
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