%A Ya Gao,Jing Mao,Chunlan Song %T Existence and Uniqueness of Solutions to the Constant Mean Curvature Equation with Nonzero Neumann Boundary Data in Product Manifold $M^{n}\times{\Bbb R}$ %0 Journal Article %D 2020 %J Acta mathematica scientia,Series A %R %P 1525-1536 %V 40 %N 6 %U {http://121.43.60.238/sxwlxbA/CN/abstract/article_16263.shtml} %8 2020-12-26 %X

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 $M^{n}\times{\Bbb R}$, where $M^{n}$ is an $n$-dimensional $(n\geq2)$ complete Riemannian manifold with nonnegative Ricci curvature, and ${\Bbb R}$ 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 with nonzero Neumann boundary data.