Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products

Assuming that there exists a translating soliton $u_\infty$ with speed $C$ in domain $\Omega$ and prescribed contact angle on $\partial\Omega$, we prove graphical solution to the mean curvature flow same converges $u_\infty +Ct$ as $t\to\infty$. We also generalize recent existence result of Gao, Ma, Wang Weng non-Euclidean settings under suitable bounds convexity Ricci $\Omega$.