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  "body": "\n## Summary\n\nA strongly pseudoconvex domain is a domain in $\\C^n$ with $C^2$ boundary whose [[Levi form|80MTNXWW80]] is positive definite at every boundary point.\nIt is also called a strictly pseudoconvex domain.\nIt is the complex analogue of a strictly convex domain.\nIn this class the analysis of [[several complex variables|BH57D2FBNR]] works best.\nThe $\\bar\\partial$-equation has good estimates, and every boundary point is locally convex after a holomorphic change of coordinates.\n\n## Explanations\n\n### L1 human\n\nA strongly pseudoconvex domain bends outwards strictly in every complex direction along its boundary.\nThe model is the unit ball in $\\C^n$.\nSmall smooth perturbations of the ball stay strongly pseudoconvex, so there are very many such domains.\nThe bidisc is not one, because its boundary contains flat complex discs, such as $\\set{(1, z_2) : \\abs{z_2} \u003c 1}$.\n",
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