  In this paper, we can prove the existence and uniqueness of solutions to the
constant mean curvature (CMC for short) equation with nonzero Neumann boundary
data in product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an
$n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci
curvature, and $\mathbb{R}$ is the Euclidean $1$-space. Equivalently, this
conclusion gives the existence of CMC graphic hypersurfaces defined over a
compact strictly convex domain $\Omega\subset M^{n}$ and having arbitrary
contact angle.
