Liouville定理的几种新证明方法

Some New Proofs of Liouville's Theorem

转变目前复变函数中证明Liouville定理主要从Cauchy积分公式入手的思路,从拓扑、多元微积分、偏微分和复变函数论等视角给出Liouville定理的几种全新证明方法,这几种证明方法在相关文献中没有见到。

Instead of applying the Cauchy integral formula to prove Liouville's theorem,this paper offers some new proofs of Liouville's theorem in view of topology,multivariate calculus,partial differential equations and theory of complex functions.Our proofs have not been found in existing literature.