本项目将选择经典复分析中的Ahlfors曲面覆盖论与现代复分析中的复动力系统的若干问题进行研究： 用球面等周不等式及对曲面进行割补的方法重新理解Ahlfors 的曲面覆盖论，并试图确定其第二基本定理中常数h的最佳值; 对相对于边界长度和在有限个给定点上的覆盖数面积达到最大值的覆盖曲面进行研究，这里的覆盖曲面可以理解成从闭单位圆盘到Riemann球面的解析映射; 在我们以往工作的基础上进一步研究高维复解析映射的隐藏在不动点的周期点的个数（即局部Dold指标）; 对超越亚纯函数的游荡域的连通数、边界结构进行研究; 对超越亚纯函数的Baker域进行细致的研究.

We will study some related problems in Ahlfors' covering surface theory and complex dynamical systems: We will use spherical isoperimetric inequalities and cutting and patching method to reinterpret Ahlfors's Theory of covering surfaces, and try to obtain the precise constant h in Ahlfors' second fundamental theorem; We will study the surfaces over the Riemann sphere with maximal area, relative to fixed boundary length and fixed covering numbers over finitely many points, and here surfaces can be interpreted to be holomorphic mappings from a closed disk into the Riemann sphere; Based on some preparation we have made we will study the numbers of periodic points hidden at fixed points of higher dimensional holomorphic mappings; For transcendental meromorphic functions, we will study the boundary and connectivity numbers of wandering Fatou domains, and will study Baker domains.