Several complex variables: local theory, Hartogs phenomena, Weierstrass theory, domains of holomorphy and pseudoconvexity
A Lean 4 formalization, on top of Mathlib, of the classical function theory of several complex variables on open subsets of finite-dimensional complex normed spaces, with values in complex Banach spaces wherever the statements allow. The compared statements cover: Cauchy's integral formula on polydiscs, Osgood's lemma, the equivalence of holomorphy and analyticity, the Cauchy-Riemann equations, Cauchy estimates, the identity theorem, the maximum modulus principle, holomorphic dependence of integrals and the Cauchy-Pompeiu identity; the theorems of Weierstrass, Montel and Vitali and an…
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