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

Existence and uniqueness of solutions to the constant mean curvature  equation with nonzero Neumann boundary data in product manifold  $M^{n}\times\mathbb{R}$