Asymptotic plateau problem in $\mathbb{H}^2x\mathbb{R}$: Tall curves

DOI10.1512/IUMJ.2023.72.9051zbMath1528.53008arXiv2006.01669OpenAlexW4383749784MaRDI QIDQ6076366

Baris Coskunuzer

Publication date: 21 September 2023

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.01669

zbMATH Keywords

symmetric spaceproduct spaceasymptotic Plateau problem

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometry of symmetric spaces (53C35)

Cites Work

• Construction of harmonic diffeomorphisms and minimal graphs
• On the asymptotic plateau problem for area minimizing surfaces in \({\mathbb{E}}(-1,\tau )\)
• Uniqueness of \(H\)-surfaces in \(\mathbb H^2 \times \mathbb R\), \(|H|\leq 1/2\), with boundary one or two parallel horizontal circles
• Complete minimal varieties in hyperbolic space
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Asymptotic Plateau problem in \(\mathbb{H}^2\times \mathbb{R}\)
• Non-properly embedded \(H\)-planes in \(\mathbb H^2\times \mathbb R\)
• Minimal surfaces with arbitrary topology in \(\mathbb{H}^2\times\mathbb{R}\)
• Properly embedded minimal annuli in \(\mathbb{H}^2 \times \mathbb{R}\)
• A Schoen theorem for minimal surfaces in \(\mathbb{H}^2 \times \mathbb{R}\)
• Properly embedded, area-minimizing surfaces in hyperbolic 3-space
• Simply Connected Minimal Surfaces with Finite Total Curvature in ℍ2 × ℝ
• The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface
• Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces
• On the asymptotic behavior of minimal surfaces in $\\mathbb{H}^2\\times\\mathbb{R}$
• Nonproper Complete Minimal Surfaces Embedded in H2 x R
• Minimal surfaces in ℍ2 × ℝ: Non-fillable curves

This page was built for publication: Asymptotic plateau problem in $\mathbb{H}^2x\mathbb{R}$: Tall curves