将解析函数的保区域定理、最大模定理和惟一性定理推广至一阶连续可微的复值函数.并进一步将其拓展到高维空间.对解析函数根点的重数、曲线的index和拓扑度进行了讨论和展望.
The open mapping theorem, the maximum modulus theorem and the uniqueness theorem are generalized from analytic functions to complex valued functions with C^1 condition. Furthermore, the same results in highdimensional space are established, the applications of the muhiplicity of root, index and degree are discussed.