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  "body": "\n## Summary\n\nA Stein manifold is a complex manifold with enough global holomorphic functions: they separate points and give compact holomorphically convex hulls of compact sets.\nStein manifolds are the complex analogue of affine varieties, and they are exactly the closed complex submanifolds of some $\\C^N$.\nOn them the main problems of several complex variables, such as the Cousin problems, are governed by topology, through Cartan's theorems A and B.\n\n## Explanations\n\n### L1 human\n\nA compact complex manifold has no nonconstant global holomorphic functions, so global function theory there is empty.\nStein manifolds are at the opposite end: global holomorphic functions are plentiful, as on $\\C^n$ itself.\nExamples are $\\C^n$, every domain of holomorphy in $\\C^n$, every open Riemann surface, and every closed complex submanifold of $\\C^n$, such as the curve $\\set{(z, w) \\in \\C^2 : w^2 = z^3 - z}$.\nThey are the natural spaces on which to do holomorphic function theory in several variables.\n",
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