乘积流形$M^{n}\times{\Bbb R}$中一类常平均曲率方程解的存在性和唯一性

Abstract

Abstract:

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.

Key words: Constant mean curvature, Neumann boundary condition, Convexity, Ricci curvature, Product manifold

CLC Number:

O186.1

Ya Gao,Jing Mao,Chunlan Song. Existence and Uniqueness of Solutions to the Constant Mean Curvature Equation with Nonzero Neumann Boundary Data in Product Manifold $M^{n}\times{\Bbb R}$[J].Acta mathematica scientia,Series A, 2020, 40(6): 1525-1536.

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References 9

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Existence and Uniqueness of Solutions to the Constant Mean Curvature Equation with Nonzero Neumann Boundary Data in Product Manifold $M^{n}\times{\Bbb R}$

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