Complex Analysis

This group gathers theorems about functions of a complex variable, the branch of analysis built on Cauchy's integral calculus for holomorphic functions. It covers the core machinery, including the Cauchy integral theorem, the residue theorem, and the maximum modulus principle, together with results on how holomorphic functions behave near singularities and at infinity, such as the Picard, Casorati-Weierstrass, and Liouville theorems, and the conformal mapping theory, including the Riemann mapping theorem, that connects complex analysis to geometry.