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  "body": "\n## Summary\n\nA plurisubharmonic exhaustion function on a complex manifold is a [[plurisubharmonic function|FF2P7ER3QT]] whose sublevel sets are relatively compact.\nIt tends to $+\\infty$ at the \"boundary\" or \"infinity\" of the manifold.\nDomains in $\\C^n$ with such a function are exactly the pseudoconvex domains.\nComplex manifolds with a smooth strictly plurisubharmonic one are exactly the Stein manifolds.\n\n## Explanations\n\n### L1 human\n\nAn exhaustion function is like a height function on a bowl.\nEach region below a given height is a compact piece, and the pieces fill up the whole space as the height grows.\nAsking the function to be plurisubharmonic means that it is subharmonic on every complex line, a complex form of convexity.\nOn $\\C^n$ the function $\\abs{z}^2$ is a plurisubharmonic exhaustion function: its sublevel sets are balls.\nOn the unit disc, $-\\log(1 - \\abs{z}^2)$ is one: it is subharmonic and blows up at the circle.\n",
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