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Classic complex analysis is built on structural function $K=1$ onlyassociated with Cauchy-Riemann equations, subsequently various generalizationsof Cauchy-Riemann equations start to break this situation. The goal of thisarticle is to show that only structural function $K=Const$ such thatLiouville's theorem is held, otherwise, it's not valid any more on complexdomain based on structural holomorphic, the correction should be $w=\Phi{{e}^{-K}}$, where $\Phi =Const$. Those theories in complex analysis which keepconstant are unable to be held as constant in the framework of structuralholomorphic. Synchronously, it deals with the generalization of Cauchy'sintegral theorem by using the new perspective of structural holomorphic, it isalso shown that some of theories in the complex analysis are special cases at$K=Const$, which are narrow to be applied such as maximum modulus principle.

Some extensive discussions of Liouville's theorem and Cauchy's integral theorem on structural holomorphic