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  "body": "\n## Summary\n\nThe Robin constant of a compact set $K$ in the plane is the least logarithmic energy of a unit charge placed on $K$.\nIt is a number in $(-\\infty, \\infty]$, and it equals $\\infty$ exactly when every unit charge on $K$ has infinite energy.\nThe [[logarithmic capacity|DBQXRTC0VN]] of $K$ is $e^{-V}$, where $V$ is the Robin constant.\nThe Robin constant also appears in the expansion at infinity of the Green function of the outside of $K$.\n\n## Explanations\n\n### L1 human\n\nSpread a unit charge on a plane conductor $K$ in the cheapest way, with the logarithmic law of repulsion.\nThe energy of this best arrangement is the Robin constant.\nA big set gives the charge room to spread, so its Robin constant is small, possibly negative.\nA single point gives no room at all, and its Robin constant is $+\\infty$.\nFor a disc of radius $r$ the Robin constant is $-\\log r$.\n",
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