A Maximum Rank Theorem for Solutions to the Homogenous Complex Monge-Ampère Equation in a $\mathbb{C}$-Convex Ring

Jingchen Hu

Suppose ${\Omega }_0,{\Omega }_1$ are two bounded strongly $\mathbb{C}$-convex domains in ${\mathbb{C}}^n$, with $n\ge 2$ and ${\Omega }_1\supset \overline{{\Omega }_0}$. Let $\mathcal{R}=Ω_1\backslash\overline{Ω_0…