  Recently Brendle-Huisken introduced a fully nonlinear flow $G$. Their aim was
to extend the surgery algorithm of Huisken-Sinestrari, into the Riemannian
setting. The aim of this paper is to go through the details on how to perform
neck detection for a closed, embedded hypersurface $M_0$ in $\mathbb{R}^{n+1}$
undergoing this $G$-flow. In order to do this we make some adjustments to
Brendle and Huiskens gradient estimate, after we have done this we can go on to
argue as in Huisken-Sinestrari's paper Mean curvature flow with surgeries of
two-convex hyperusrfaces, in order to classify two-convex surfaces undergoing
$G$-flow.
