乘积流形$M^{n}\times\mathbb{R}$中具有非零Neumann边界的常中曲率方程解的存在唯一性
Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$
摘要：
本文证明了乘积流形$M^{n}\times\mathbb{R}$中具有非零Neumann边界数据的常中曲率（CMC）方程解的存在唯一性，其中$M^{n}$是具有非负Ricci曲率的$n$维（$n\geq2$）完备黎曼流形，$\mathbb{R}$是欧氏$1$ -空间.等价地，这个结论给出了定义在紧严格凸区域$Ω\subset M^{n}$上的具有任意接触角的CMC图超曲面的存在性。
英文摘要：
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 $Ω\subset M^{n}$ and having arbitrary contact angle.
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