Minimal surfaces in \(\widehat PSL_2(\mathbb R)\)

zbMath1235.53064arXiv1002.4647MaRDI QIDQ648761

Rami Younes

Publication date: 28 November 2011

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4647

zbMATH Keywords

gradient estimatehomogeneous Riemannian manifoldsminimal graphs

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)

Related Items

The Dirichlet problem for the minimal surface equation in \(\mathrm{Sol}_{3}\), with possible infinite boundary data ⋮ Construction of minimal annuli in \(\widetilde{\mathrm{PSL}}_2(\mathbb{R},\tau)\) via a variational method ⋮ Conjugate plateau constructions in product spaces ⋮ 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 graphs in \(\mathrm{Nil}_3:\) existence and non-existence results ⋮ On complete constant mean curvature vertical multigraphs in \(\mathbb E(\kappa,\tau)\) ⋮ Minimal graphs in \(\widetilde{\mathrm{PSL}_2(\mathbb R)}\) over unbounded domains ⋮ The Jenkins-Serrin problem for translating horizontal graphs in \(M\times\mathbb{R}\) ⋮ Classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces ⋮ On the asymptotic plateau problem in \(\widetilde{\mathrm{SL}}_2 (\mathbb{R})\) ⋮ The Dirichlet problem for the constant mean curvature equation in \(\operatorname{Sol}_3\) ⋮ On the asymptotic plateau problem for area minimizing surfaces in \({\mathbb{E}}(-1,\tau )\)

Cites Work

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• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Le problème de Dirichlet pour l'équation des surfaces minimales sur des domaines non bornés
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