Minimal surfaces with positive genus and finite total curvature in \(\mathbb{H}^2 \times \mathbb{R}\)

DOI10.2140/GT.2014.18.141zbMath1280.49062arXiv1208.5253OpenAlexW3124669956MaRDI QIDQ389977

M. Magdalena Rodríguez, Francisco Martín, Rafe R. Mazzeo

Publication date: 22 January 2014

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5253

zbMATH Keywords

finite total curvaturemoduli spacesminimal surfacesgluing constructionspositive genus

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)

Related Items (14)

Minimal surfaces in ℍ2 × ℝ: Non-fillable curves ⋮ A Schoen theorem for minimal surfaces in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Asymptotic Plateau problem in \(\mathbb{H}^2\times \mathbb{R}\) ⋮ Free boundaries surfaces and saddle towers minimal surfaces in \(\mathbb{S}^2 \times \mathbb{R}\) ⋮ On doubly periodic minimal surfaces in \(\mathbb H^2 \times\mathbb R\) with finite total curvature in the quotient space ⋮ Construction of minimal annuli in \(\widetilde{\mathrm{PSL}}_2(\mathbb{R},\tau)\) via a variational method ⋮ Conjugate plateau constructions in product spaces ⋮ GENUS MINIMAL k-NOIDS AND SADDLE TOWERS IN ⋮ Uniform a priori estimates for a class of horizontal minimal equations ⋮ A geometrical correspondence between maximal surfaces in anti-de Sitter space-time and minimal surfaces in \(\mathbb H^2\times\mathbb R\) ⋮ On the characterization of minimal surfaces with finite total curvature in \({\mathbb {H}}^2\times {\mathbb {R}}\) and \(\widetilde{\mathrm{PSL}}_2 ({\mathbb {R}})\) ⋮ Minimal surfaces with arbitrary topology in \(\mathbb{H}^2\times\mathbb{R}\) ⋮ On the asymptotic plateau problem in \(\widetilde{\mathrm{SL}}_2 (\mathbb{R})\) ⋮ Properly embedded minimal annuli in \(\mathbb{H}^2 \times \mathbb{R}\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction of harmonic diffeomorphisms and minimal graphs
• New complete embedded minimal surfaces in \({\mathbb {H} ^2\times \mathbb {R}}\)
• Parabolic stable surfaces with constant mean curvature
• Associate and conjugate minimal immersions in \(M \times R\)
• Complete minimal varieties in hyperbolic space
• Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Elliptic partial differential equations of second order
• Related aspects of positivity in Riemannian geometry
• Resolvents and Martin boundaries of product spaces
• The moduli space of complete embedded constant mean curvature surfaces
• Connected sums of constant mean curvature surfaces in Euclidean 3 space
• The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface
• A Costa-Hoffman-Meeks type surface in $\mathbb H^{2} \times\mathbb R $
• Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces
• The space of complete minimal surfaces with finite total curvature as lagrangian submanifold
• Moduli Spaces of Singular Yamabe Metrics
• The Dirichlet problem for the minimal surface equation, with infinite data
• Saddle towers and minimal k-noids in ℍ² × ℝ

This page was built for publication: Minimal surfaces with positive genus and finite total curvature in \(\mathbb{H}^2 \times \mathbb{R}\)