The Dirichlet problem for the minimal hypersurface equation in \(M \times \mathbb R\) with prescribed asymptotic boundary

DOI10.1016/j.matpur.2009.08.002zbMath1193.58012OpenAlexW2022012360MaRDI QIDQ846997

Nedir do Espírito-Santo, Susana Fornari, Jaime Bruck Ripoll

Publication date: 16 February 2010

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2009.08.002

zbMATH Keywords

Dirichlet problemminimal hypersurfaceproduct spaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Boundary value problems on manifolds (58J32) Quasilinear elliptic equations with mean curvature operator (35J93)

Related Items (6)

An interior gradient estimate for the mean curvature equation of Killing graphs and applications ⋮ Recent rigidity results for graphs with prescribed mean curvature ⋮ Some existence results on the exterior Dirichlet problem for the minimal hypersurface equation ⋮ Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures ⋮ Survey on the asymptotic Dirichlet problem for the minimal surface equation ⋮ Regularity at infinity of Hadamard manifolds with respect to some elliptic operators and applications to asymptotic Dirichlet problems

Cites Work

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• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Interior gradients estimates and existence theorems for constant mean curvature graphs in \(M^n\times\mathbb R\)
• The theory of minimal surfaces in \(M\times \mathbb R\)
• An extension of a theorem of Serrin to graphs in warped products

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