Maximum Principles and Consequences for $\gamma$-translators in $\mathbb{R}^{n+1}$ II

This paper focuses on the translating solitons of fully nonlinear extrinsic curvature geometric flows in $\mathbb{R}^{n+1}$. We present a generalization of the Spruck-Xiao's and Spruck-Sun's convexity results for $1$-homogeneous convex/concave curvature functions, and further provide several characterizations of the family of grim reaper cylinders under curvature constraints.