A halfspace theorem for mean curvature \(H = \frac 12\) surfaces in \(\mathbb H^2 \times \mathbb R\)

DOI10.1016/j.jmaa.2009.10.031zbMath1191.53045OpenAlexW2000323107MaRDI QIDQ847761

Barbara Nelli, Ricardo Sa Earp

Publication date: 19 February 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.10.031

zbMATH Keywords

maximum principlemean curvaturesecond order elliptic equationhalfspace theoremvertical end

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (10)

Existence of vertical ends of mean curvature $1/2$ in $\mathbb{H}^{2} ×\mathbb{R}$ ⋮ Bi-Halfspace and Convex Hull Theorems for Translating Solitons ⋮ Invariant surfaces in \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R, \tau)\) and applications ⋮ Slab theorem and halfspace theorem for constant mean curvature surfaces in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Existence of barriers for surfaces with prescribed curvatures in \(\mathbb M^ 2{\times}\mathbb R\) ⋮ Uniqueness of \(H\)-surfaces in \(\mathbb H^2 \times \mathbb R\), \(|H|\leq 1/2\), with boundary one or two parallel horizontal circles ⋮ A half-space theorem for ideal Scherk graphs in \(M \times \mathbb R\) ⋮ The half space property for cmc 1/2 graphs in \(\mathbb {E}(-1,\tau )\) ⋮ A half-space theorem for graphs of constant mean curvature \(0<H<\frac{1}{2}\) in \(\mathbb{H}^{2}\times\mathbb{R}\) ⋮ Half-space type theorem for translating solitons of the mean curvature flow in Euclidean space

Cites Work

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• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern
• The strong halfspace theorem for minimal surfaces
• Screw motion surfaces in \(\mathbb H^2 \times \mathbb R\) and \(\mathbb S^2\times \mathbb R\)
• Uniqueness of \(H\)-surfaces in \(\mathbb H^2 \times \mathbb R\), \(|H|\leq 1/2\), with boundary one or two parallel horizontal circles
• An asymptotic theorem for minimal surfaces and existence results for minimal graphs in \({\mathbb H^2 \times \mathbb R}\)
• Global properties of constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\)
• On complete mean curvature \(\frac 12\) surfaces in \(\mathbb{H}^2\times\mathbb{R}\)
• PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ²×ℝ

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