Half-space theorems for minimal surfaces in \(\mathrm{Nil}_3\) and \(\mathrm{Sol}_3\)

DOI10.4310/JDG/1317758868zbMath1237.53053arXiv1005.3963OpenAlexW4299952785WikidataQ115170742 ScholiaQ115170742MaRDI QIDQ661931

Benoît Daniel, Harold Rosenberg, William Hamilton III Meeks

Publication date: 11 February 2012

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3963

zbMATH Keywords

minimal surfaceHeisenberg groupsolvable Lie groupleft-invariant metrics

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (9)

Some half-space theorems in the real projective space ⋮ Simons type formulas for surfaces in Sol₃ and applications ⋮ A half-space theorem for ideal Scherk graphs in \(M \times \mathbb R\) ⋮ The half space property for cmc 1/2 graphs in \(\mathbb {E}(-1,\tau )\) ⋮ A half-space theorem for graphs of constant mean curvature \(0<H<\frac{1}{2}\) in \(\mathbb{H}^{2}\times\mathbb{R}\) ⋮ The geometry of stable minimal surfaces in metric Lie groups ⋮ Half-space theorems for properly immersed surfaces in \(\mathbb{R}^3\) with prescribed mean curvature ⋮ The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones ⋮ Half-space type theorem for translating solitons of the mean curvature flow in Euclidean space

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