论文标题
管子，离散的汇总产品和径向投影之间的交点
Intersection between pencils of tubes, discretized sum-product, and radial projections
论文作者
论文摘要
在本文中，我们证明了平面中的以下结果。他们彼此相关，而每个人都有自己的兴趣。 首先，在非浓度条件下，我们在$δ$ tubes的铅笔之间获得了$ε_0$启动。实际上，我们表明它等同于离散的总和问题问题，因此$ε_0$遵循了波尔加因的著名结果。 然后，我们证明了有关径向预测的几个新结果。我们还讨论了$ε_0$的依赖性并做出新的猜想。 仔细细化后，还给出了霜冻措施的管条件。
In this paper we prove the following results in the plane. They are related to each other, while each of them has its own interest. First we obtain an $ε_0$-increment on intersection between pencils of $δ$-tubes, under non-concentration conditions. In fact we show it is equivalent to the discretized sum-product problem, thus the $ε_0$ follows from Bourgain's celebrated result. Then we prove a couple of new results on radial projections. We also discussion about the dependence of $ε_0$ and make a new conjecture. A tube condition on Frostman measures, after careful refinement, is also given.
