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  "body": "\n## Summary\n\nA Reinhardt domain is a domain in $\\C^n$ that is unchanged when each coordinate is rotated by its own angle.\nSuch a domain is determined by the set of absolute values $(\\abs{z_1}, \\dots, \\abs{z_n})$ of its points.\n[[Polydiscs|DJBWP7D3M8]] and the [[unit ball|PDQ9KW9FAP]] are Reinhardt domains.\nThey are the natural domains of convergence of [[power series in several variables|R3QTCPTJK7]].\nThey also give the first examples of the extension phenomena of [[several complex variables|BH57D2FBNR]].\n\n## Explanations\n\n### L1 human\n\nMultiply the first coordinate of a point by $e^{i\\theta_1}$, the second by $e^{i\\theta_2}$, and so on.\nThis turns each coordinate around the origin of its own complex plane without changing its size.\nA Reinhardt domain contains, with each point, all the points obtained in this way.\nSo one can draw it as a region in the \"absolute value space\" of points $(\\abs{z_1}, \\dots, \\abs{z_n})$, which is a part of $[0, \\infty)^n$.\nFor example, the unit polydisc of $\\C^2$ is drawn as the square $[0, 1) \\times [0, 1)$, and the unit ball as a quarter of a disc.\n",
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