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

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 $M^n\times \mathbb{R}$, where $M^n$ is an $n$-dimensional ($n\ge 2$) 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 $\Omega \subset M^n$ and having arbitrary contact angle.

12 pages. Comments are welcome. arXiv admin note: substantial text overlap with arXiv:2001.09860

References in corpus (3)

• The half-space property and entire positive minimal graphs in M x R
• Periodic constant mean curvature surfaces in H^2 x R
• Translating solutions of the nonparametric mean curvature flow with nonzero Neumann boundary data in product manifold $M^n\times \mathbb{R}$