论文标题
$ \ mathbb {r}^n $中径向投影的特殊集估计值
Exceptional set estimates for radial projections in $\mathbb{R}^n$
论文作者
论文摘要
我们在本文中证明了两个猜想。 第一个猜想是由隆德（Lund），pham和thu撰写的：给定一个borel套装$ a \ subset \ mathbb {r}^n $ \ Mathbb {r}^n \ setMinus a \ mid \ text {dim}（π_y（a））<s \}）\ leq \ max \ max \ {k+s- \ s- \ s- \ dim a，0 \}。 \ text {dim}（\ {x \ in \ mathbb {r}^n \ setMinus a \ mid \ text {dim}（π_x（a））<\ text {dim} a \} a \}）
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 $0<s<k$, we have \[ \text{dim}(\{y\in \mathbb{R}^n \setminus A\mid \text{dim} (π_y(A)) < s\})\leq \max\{k+s -\dim A,0\}. \] The second conjecture is by Liu: Given a Borel set $A\subset \mathbb{R}^n$, then \[ \text{dim} (\{x\in \mathbb{R}^n \setminus A \mid \text{dim}(π_x(A))<\text{dim} A\}) \leq \lceil \text{dim} A\rceil. \]
