论文标题
有限空间中的径向投影定理
Radial projection theorems in finite spaces
论文作者
论文摘要
在径向预测和对著名的Falconer距离问题应用程序的结果方面的动机，我们研究了有限领域的径向预测。更确切地说，由于Mattila和Orponen（2016），Orponen（2018）和Liu（2020），我们将结果扩展到有限的空间。在某些情况下，我们的结果比连续环境中的相应结果更强。特别是，我们解决了由于Liu和Orponen引起的猜想的有限场类似物，该猜想是在$ d-2 $和$ d-1 $之间的一组尺寸的一组径向预测上。
Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen (2016), Orponen (2018), and Liu (2020) to finite spaces. In some cases, our results are stronger than the corresponding results in the continuous setting. In particular, we solve the finite field analog of a conjecture due to Liu and Orponen on the exceptional set of radial projections of a set of dimension between $d-2$ and $d-1$.
