Uniqueness of minimal surfaces whose boundary is a horizontal graph and some Bernstein problems in \({{\mathbb{H}^{2}\times \mathbb{R}}}\)

DOI10.1007/s00209-012-1001-4zbMath1258.53063OpenAlexW2066266989MaRDI QIDQ1936628

Ricardo Sa Earp

Publication date: 6 February 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-012-1001-4

zbMATH Keywords

maximum principleconvex domainPlateau problemBernstein problemhorizontal minimal equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items

A Schoen theorem for minimal surfaces in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Uniform a priori estimates for a class of horizontal minimal equations ⋮ Properly embedded surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\)

Cites Work

• Unnamed Item
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Minimal surfaces of Riemann type in three-dimensional product manifolds
• An asymptotic theorem for minimal surfaces and existence results for minimal graphs in \({\mathbb H^2 \times \mathbb R}\)
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• The problem of Plateau on a Riemannian manifold
• 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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