  A translating soliton is a hypersurface $M$ in $\mathbb{R}^{n+1}$ such that
the family $M_t= M- t \,\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such
that normal component of the velocity at each point is equal to the mean
curvature at that point $\mathbf{H}=\mathbf{e}_{n+1}^{\perp}.$ In this paper we
obtain a characterization of hyperplanes which are parallel to
$\mathbf{e}_{n+1}$ and the family of tilted grim reaper cylinders as the only
translating solitons in $\mathbb{R}^{n+1}$ which are $C^1$-asymptotic to two
half-hyperplanes outside a non-vertical cylinder. This result was proven for
translators in $\mathbb{R}^3$ by the second author, Perez-Garcia, Savas-Halilaj
and Smoczyk under the additional hypotheses that the genus of the surface was
locally bounded and the cylinder was perpendicular to the translating velocity.

Differential Geometry