Dimension of the minimum set for the real and complex Monge-Ampère equations in critical Sobolev spaces

Tristan C. Collins, Connor Mooney

We prove that the zero set of a nonnegative plurisubharmonic function that solves $\det (\partial \overline{\partial }u)\ge 1$ in ${\mathbb{C}}^n$ and is in $W^{2, \frac{n(n-k)}{k}…