Example 15.21.1541D1398D77FC

Example 15.21.15.41D1398D77FC On the bidisk in $\mathbb C^2$ with coordinates $(z,w)$, the function

is locally Lipschitz, plurisubharmonic and not $C^1$ along $\{ z=0\} $. Plurisubharmonicity follows by writing its two summands as convex exponential compositions of $\log |z|$ and $\log |z|+\log |w|^2$. At $z\ne 0$,

Hence $\det (H_{j\bar k})=1$, and pluripolar nullity gives $(\mathrm{dd}^{\mathrm{c}}H)^2=2\pi ^{-2}\, \mathrm{d}\Lambda $ on the entire bidisk.