高维space-filling问题及其相关问题

1998 年，Strichartz等人研究Sierpinski垫上的Cauchy变换，并提出了Cantor集猜想和space-filling猜想。Younsi把space-filling猜想的第一个等式推广到了平面上的解析函数代数。 ..本项目将研究space-filling猜想在高维的推广，研究内容包括高维space-filling问题, space-filling猜想的第二个等式及其推广。我们的研究工具包括拓扑度、解析容量、分形几何数理论以及Riesz变换等理论。本项目的特色在于复分析和分形几何结合研究，引入了拓扑度来研究经典复分析中问题并取得了很好的效果。

In 1998, Strichertz et al. studied the Cauchy transform on the Sierpinski gasket, they proposed two conjectures: Cantor set conjecture and space-filling conjecture. Younsi extended the first equation of the space-filling conjecture to the algebras of analytic functions on the plane. ..This project will study the generalization of space-filling conjecture in high-dimensional space, including the high-dimensional space-filling problem, the second equation of the space-filling conjecture and its generalization. Our research tools include topological degree, analytic capacity, fractal geometry, Riesz transform and so on. The feature of this project is the combination of complex analysis and fractal geometry. It uses topological degree to study the problems in classical complex analysis and achieves good effect.