Cauchy积分公式与Möbius变换是函数论的两个重要研究对象和有力工具。Clifford分析是现代函数论的热门领域之一。本项目拟研究以下几个问题：.(1)研究Clifford分析中双hypergenic函数的Cauchy积分公式；.(2)研究双hypergenic函数与高维空间偏微分方程组之间的关系及其相关算子的性质；.(3)研究Clifford Möbius变换的重要性质；.(4)研究Clifford Möbius变换在求解方程、几何问题以及信号处理中的应用。.该项目的研究将进一步丰富和完善Clifford分析中的相关理论，具有重要的理论意义和应用价值。

Cauchy integral formula and Möbius transformations are two important research objects and power tools in function theory. Clifford analysis is one of the hot fields of modern function theory. The project is to study the following aspects: .(1)To study Cauchy integral formula for bihypergenic functions in Clifford analysis;.(2)To discuss the relationship between bihypergenic functions and partial differential equations in higher dimensional space, and to study some properties of the related operators to bihypergenic functions;.(3)To study important properties of Clifford Möbius transformations;.(4)To study some applications of Clifford Möbius transformations in solving equations, geometric problems and signal processing..The project will further enrich and perfect the related theory in Clifford analysis and it is significant in both theory and practice.