Invariant surfaces in \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R, \tau)\) and applications

DOI10.1007/s00574-012-0026-yzbMath1261.53060OpenAlexW1984057240MaRDI QIDQ1928352

Carlos Peñafiel

Publication date: 3 January 2013

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-012-0026-y

zbMATH Keywords

minimal surfacesconstant mean curvatureone-parameter group of isometriessurfaces invariant by isometries

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

Constant mean curvature isometric immersions into \(\mathbb{S}^2\times\mathbb{R}\) and \(\mathbb{H}^2\times\mathbb{R}\) and related results ⋮ Construction of minimal annuli in \(\widetilde{\mathrm{PSL}}_2(\mathbb{R},\tau)\) via a variational method ⋮ Parabolicity of invariant surfaces ⋮ Height estimates for \(H\)-surfaces in the warped product \({\mathbb {M}}\times _{f} {\mathbb {R}}\) ⋮ On the characterization of minimal surfaces with finite total curvature in \({\mathbb {H}}^2\times {\mathbb {R}}\) and \(\widetilde{\mathrm{PSL}}_2 ({\mathbb {R}})\) ⋮ The slab theorem for minimal surfaces in \(\mathbb {E}(-1,\tau)\) ⋮ Immersed hyperbolic and parabolic screw motion surfaces in the space \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R,\tau)\) ⋮ On the asymptotic plateau problem in \(\widetilde{\mathrm{SL}}_2 (\mathbb{R})\) ⋮ On the asymptotic plateau problem for area minimizing surfaces in \({\mathbb{E}}(-1,\tau )\)

Cites Work

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• Screw motion surfaces in \(\mathbb H^2 \times \mathbb R\) and \(\mathbb S^2\times \mathbb R\)
• A halfspace theorem for mean curvature \(H = \frac 12\) surfaces in \(\mathbb H^2 \times \mathbb R\)
• Isometric immersions into 3-dimensional homogeneous manifolds
• 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 \({\mathbb H^2 \times \mathbb R}\)
• Invariant surfaces of the Heisenberg groups
• The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface
• PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ²×ℝ

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