{"id":"palomar/PALOMAR-2026-09-18-000008","url":"https://github.com/bjbraams/lean-SCV/tree/336759b3964011aa0d6e1111e32276b1476fb7f0","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-18-000008-v1.json","repo":"https://github.com/bjbraams/lean-SCV","tags":["math.CV","msc:32A10","msc:32A05","msc:32D05","msc:32D15","msc:32D20","msc:32B05","msc:32U05","msc:68V20","complex-analysis"],"score":0,"title":"Several complex variables: local theory, Hartogs phenomena, Weierstrass theory, domains of holomorphy and pseudoconvexity","trust":"high","domain":"math.CV","source":"palomar","authors":["Bastiaan J Braams"],"reviews":0,"subject":"math.CV","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-18","reactions":{},"formalized":true,"formalizes":[{"title":"Holomorphic Functions and Integral Representations in Several Complex Variables","identifier":"Graduate Texts in Mathematics 108, Springer, 1986","relationship":"adapts"},{"title":"An Introduction to Complex Analysis in Several Variables","identifier":"2nd edition, North-Holland Mathematical Library 7, North-Holland, 1973","relationship":"adapts"},{"title":"From Holomorphic Functions to Complex Manifolds","identifier":"Graduate Texts in Mathematics 213, Springer, 2002","relationship":"adapts"},{"title":"Lectures on Holomorphic Functions of Several Complex Variables","identifier":"Jagiellonian University manuscript, 1997-2021","relationship":"adapts"},{"title":"Introduction to Complex Analysis in Several Variables","identifier":"Birkhäuser, 2005","relationship":"adapts"}]}