Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold Mⁿ×ℝ

2020/01/30 by Ya Gao, Jing Mao, Gao, Ya +3
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2001.11840

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 Mⁿ×ℝ, where Mⁿ is an n-dimensional (n≥2) complete Riemannian manifold with nonnegative Ricci curvature, and ℝ is the Euclidean 1-space. Equivalently, this conclusion gives the existence of CMC graphic hypersurfaces defined over a compact strictly convex domain Ω⊂ Mⁿ and having arbitrary contact angle.

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