Travelling graphs for the forced mean curvature motion in an arbitrary space dimension

We construct travelling wave graphs of the form $z=-ct+\varphi (x)$, $\phi: x \in $\mathbb{R}$^{N-1} \mapsto \phi(x)\in $\mathbb{R}$$,$N \geq 2$,solutionstothe$N$-dimensionalforcedmeancurvaturemotion$V_n=-c_0+\kappa$($c\geq c_0$) with prescribed asymptotics. For any 1-homogeneous function ${\varphi }_{\mathrm{\infty }}$, viscosity solution to the eikonal equation $\mathrm{\mid }D{\varphi }_{\mathrm{\infty }}\mathrm{\mid }=\sqrt{(c\mathrm{/}{c}_0{)}^2-1}$, we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by ${\varphi }_{\mathrm{\infty }}$. We also describe ${\varphi }_{\mathrm{\infty }}$ in terms of a probability measure on ${\mathbb{S}}^{N-2}$.