Curvature integral on convex hypersurfaces

Let $M^n$, $n\ge3$, be the smooth, connected, complete, noncompact boundary of a closed convex set with nonempty interior in $\mathbb{R}^{n+1}$. We prove that its normalized scalar-curvature integral at infinity is at most $4πω_{n-2}(1-\operatorname{AVR}(M))$, except when, up to an ambient rigid mot