= Positivity criterion for a radial Kähler potential
{title2=$u''(t)>0,\quad\lim_{t\to-\infty}e^{-t}u''(t)>0$}
For a potential already smooth on all of $\mathbb C$, the associated form is a <Kähler form> exactly when the displayed two positivity conditions hold. The first gives a positive metric coefficient off the origin; the second is positivity of $f_{z\bar z}(0)$. The associated real metric is $2f_{z\bar z}(dx^2+dy^2)$. Positivity away from the origin alone permits a degenerate metric at the origin.
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