Survey on the asymptotic Dirichlet problem for the minimal surface equation

DOI10.1007/978-3-030-68541-6_7zbMath1484.53007arXiv1909.08437OpenAlexW2974216355MaRDI QIDQ2065855

Esko Heinonen

Publication date: 13 January 2022

Full work available at URL: https://arxiv.org/abs/1909.08437

zbMATH Keywords

minimal surfacesHadamard manifoldsasymptotic Dirichlet problem

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) PDEs on manifolds (35R01)

Related Items (1)

Recent rigidity results for graphs with prescribed mean curvature

Cites Work

• Unnamed Item
• An interior gradient estimate for the mean curvature equation of Killing graphs and applications
• The half-space property and entire positive minimal graphs in \(M \times \mathbb{R}\).
• Some existence results on the exterior Dirichlet problem for the minimal hypersurface equation
• Function theory on manifolds which possess a pole
• Construction of harmonic diffeomorphisms and minimal graphs
• Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems
• Complete minimal graphs with prescribed asymptotic boundary on rotationally symmetric Hadamard surfaces
• The Dirichlet problem at infinity for manifolds of negative curvature
• The Dirichlet problem for the minimal hypersurface equation in \(M \times \mathbb R\) with prescribed asymptotic boundary
• Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds
• Killing graphs with prescribed mean curvature
• An asymptotic theorem for minimal surfaces and existence results for minimal graphs in \({\mathbb H^2 \times \mathbb R}\)
• Asymptotic Dirichlet problem on negatively curved spaces
• Gap theorems for noncompact Riemannian manifolds
• Positive harmonic functions on complete manifolds of negative curvature
• Brownian motion and harmonic functions on rotationally symmetric manifolds
• The Dirichlet problem at infinity for nonpositively curved manifolds
• The nonsolvability of the Dirichlet problem on negatively curved manifolds
• Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Elliptic partial differential equations of second order
• On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold
• Some remarks on the prescribed mean curvature equation on complete manifolds.
• Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures
• Asymptotic Dirichlet problems in warped products
• On the asymptotic Dirichlet problem for a class of mean curvature type partial differential equations
• Asymptotic Dirichlet problem for \(\mathcal{A}\)-harmonic and minimal graph equations in Cartan-Hadamard manifolds
• Dirichlet problem for \(f\)-minimal graphs
• Local behavior of solutions of quasi-linear equations
• Visibility manifolds
• The theory of minimal surfaces in \(M\times \mathbb R\)
• An extension of a theorem of Serrin to graphs in warped products
• Existence and non-existence for a mean curvature equation in hyperbolic space
• A note on minimal graphs over certain unbounded domains of Hadamard manifolds
• Dirichlet problem at infinity for \(\mathcal A\) -harmonic functions
• Minimal surfaces and harmonic diffeomorphisms from the complex plane onto certain Hadamard surfaces
• Asymptotic Dirichlet Problems for Harmonic Functions on Riemannian Manifolds
• On Harnack's theorem for elliptic differential equations
• A Note on the Dirichlet Problem at Infinity for Manifolds of Negative Curvature
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• On Deciding Whether a Surface is Parabolic or Hyperbolic
• Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds
• Existence and non-existence of minimal graphic and p-harmonic functions
• Regularity at infinity of Hadamard manifolds with respect to some elliptic operators and applications to asymptotic Dirichlet problems
• The Dirichlet problem for the minimal surface equation in higher dimensions.
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
• Manifolds of Negative Curvature

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