Sharp conditions for fully nonlinear equations with $(n-1)$-Hessian matrix: Part I. Monge--Ampère case

We study positive $(n-1)$-convex entire subsolutions of the normalized real $(n-1)$ Monge--Ampère equation $\operatorname{det}^{\frac1n}\bigl(ΔuI-D^2u\bigr)=f(u)+g(u)|Du|^q$ in $\mathbb R^n$. Under two sets of structural assumptions on the continuous, non-decreasing coefficients $f$ and $g$, we esta