论文标题
圆圈的furstenberg型问题，而Kaufman-type限制了投影定理，$ \ mathbb {r}^3 $
A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb{R}^3$
论文作者
论文摘要
我们解决了Fässler和Orponen的猜想，这是在$ \ Mathbb {r}^3 $中以空格曲线索引的一维子空间的特殊预测的尺寸。我们通过获得与Sogge的Cinematic Curvature条件相关的$ C^2 $曲线的分形曲线的变体中的变体中获得尖锐的$ l^p $边界。一个关键的新工具是使用离散几何形状的镜头切割技术。
We resolve a conjecture of Fässler and Orponen on the dimension of exceptional projections to one-dimensional subspaces indexed by a space curve in $\mathbb{R}^3$. We do this by obtaining sharp $L^p$ bounds for a variant of the Wolff circular maximal function over fractal sets for a class of $C^2$ curves related to Sogge's cinematic curvature condition. A key new tool is the use of lens cutting techniques from discrete geometry.
