Embedded 𝐻-planes in hyperbolic 3-space

DOI10.1090/tran/7286zbMath1475.53067arXiv1705.02951OpenAlexW3104477085MaRDI QIDQ4561835

Baris Coskunuzer

Publication date: 13 December 2018

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

Full work available at URL: https://arxiv.org/abs/1705.02951

zbMATH Keywords

homotopy classJordan curveminimizing\( H\)-plane\( H\)-surfacequasi-Fuchsian hyperbolic \( 3\)-manifold

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) General geometric structures on low-dimensional manifolds (57M50)

Related Items (2)

Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces ⋮ Asymptotic Plateau problem for prescribed mean curvature hypersurfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic \(H\)-Plateau problem in \(\mathbb H^3\)
• Non-properly embedded \(H\)-planes in \(\mathbb{H}^3\)
• Quasi-Fuchsian 3-manifolds and metrics on Teichmüller space
• Complete minimal graphs with prescribed asymptotic boundary on rotationally symmetric Hadamard surfaces
• Complete minimal hypersurfaces in hyperbolic n-manifolds
• Complete minimal varieties in hyperbolic space
• Topology of three dimensional manifolds and the embedding problems in minimal surface theory
• The existence of embedded minimal surfaces and the problem of uniqueness
• Stable constant mean curvature surfaces minimize area
• Existence and regularity of constant mean curvature hypersurfaces in hyperbolic space
• Embeddedness of the solutions to the \(H\)-Plateau problem
• The Plateau problem for surfaces of prescribed mean curvature in a Riemannian manifold
• Minimal discs in hyperbolic space bounded by a quasicircle at infinity
• Minimizing constant mean curvature hypersurfaces in hyperbolic space
• On almost-Fuchsian manifolds
• The Existence of Least Area Surfaces in 3-Manifolds
• Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces
• Generic uniqueness of area minimizing disks for extreme curves
• Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
• Entropy, minimal surfaces and negatively curved manifolds
• Counting minimal surfaces in quasi-Fuchsian three-manifolds
• Asymptotic Plateau Problem
• On the plateau problem for surfaces of constant mean curvature
• Two‐dimensional variational problems with obstructions, and Plateau's problem for h‐surfaces in a riemannian manifold
• Uniformization, Moduli, and Kleinian Groups†
• On the geometric and topological rigidity of hyperbolic 3-manifolds

This page was built for publication: Embedded 𝐻-planes in hyperbolic 3-space