Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

DOI10.1090/S0002-9947-09-04645-5zbMath1181.53051arXiv0705.1436OpenAlexW2079088760MaRDI QIDQ3642691

Pablo Mira, Isabel Fernández

Publication date: 6 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.1436

zbMATH Keywords

Heisenberg groupminimal graphsholomorphic quadratic differentialBernstein problem

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) Non-Euclidean differential geometry (53A35)

Related Items

Timelike minimal surfaces in the three-dimensional Heisenberg group, Compact stable surfaces with constant mean curvature in Killing submersions, Minimal cylinders in the three-dimensional Heisenberg group, Conjugate plateau constructions in product spaces, Uniqueness of constant mean curvature spheres, Parabolic stable surfaces with constant mean curvature, Dual quadratic differentials and entire minimal graphs in Heisenberg space, Gauss maps of the surfaces in the three-dimensional Heisenberg group, Constant mean curvature surfaces in \({\mathbb {M}}^2(c)\times \mathbb {R}\) and finite total curvature, Height and area estimates for constant mean curvature graphs in \(\mathbb {E}(\kappa ,\tau )\)-spaces, On complete constant mean curvature vertical multigraphs in \(\mathbb E(\kappa,\tau)\), The Gauss map of surfaces in \(\widetilde{\mathrm {PSL}}_2(\mathbb R)\), The half space property for cmc 1/2 graphs in \(\mathbb {E}(-1,\tau )\), An extension of Ruh-Vilms’ theorem to hypersurfaces in symmetric spaces and some applications, The geometry of stable minimal surfaces in metric Lie groups, The classical theory of minimal surfaces, Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group

Cites Work

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• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Construction of harmonic diffeomorphisms and minimal graphs
• Isometric immersions into 3-dimensional homogeneous manifolds
• A Weierstrass representation formula for minimal surfaces in \(\mathbb H_{3}\) and \(\mathbb H^{2} \times \mathbb R\)
• Constant mean curvature surface, harmonic maps, and universal Teichmüller space
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Invariant surfaces of the Heisenberg groups
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• The Dirichlet problem for constant mean curvature surfaces in Heisenberg space
• The Cauchy problem for the Liouville equation and Bryant surfaces
• A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
• The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
• Half-space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group
• Parabolic Constant Mean Curvature Spacelike Surfaces
• Harmonic maps and constant mean curvature surfaces in H 2 x R