  In this paper, several results regarding $\gamma$-translators in
$\mathbb{R}^{n+1}$ are obtained by means of maximum principle arguments. The
paper delves into characterizations of grim reaper cylinders and establishes
convexity results for translators in $\mathbb{R}^3$. Finally, it discusses the
property of bounded extrinsic geometry in terms of the function $H\gamma^{-1}$.
