A stability result for translating spacelike graphs in Lorentz manifolds

DOI10.1007/s10473-024-0206-zarXiv2101.05447OpenAlexW4391568250MaRDI QIDQ6192410

Jing Mao, Ya Gao, Chuan Xi Wu

Publication date: 11 March 2024

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.05447

zbMATH Keywords

mean curvature flowconstant mean curvatureLorentz manifoldsspacelike graphsmaximal spacelike graphstranslating spacelike graphs

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Cites Work

• The half-space property and entire positive minimal graphs in \(M \times \mathbb{R}\).
• Periodic constant mean curvature surfaces in \(\mathbb{H}^2 \times \mathbb{R}\)
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Curvature estimates for minimal hypersurfaces
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• The boundary behavior of domains with complete translating, minimal and CMC graphs in \(N^2\times\mathbb{R}\)
• Curvature estimates for CMC surfaces in three dimensional manifolds
• Asymptotic shape of cusp singularities in curve shortening
• Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold \(M^2\times\mathbb{R}\)
• Translating graphs by mean curvature flow
• Stable minimal surfaces in \(M\times \mathbb R\)
• Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$
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