Simply connected constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\)

DOI10.1307/mmj/1163789914zbMath1152.53307OpenAlexW2057199115WikidataQ125945635 ScholiaQ125945635MaRDI QIDQ956719

Harold Rosenberg, Barbara Nelli

Publication date: 26 November 2008

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1163789914

zbMATH Keywords

entire graphsround sphereproperly embedded \(H\)-surfaces

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 (8)

Constant mean curvature graphs on exterior domains of the hyperbolic plane ⋮ Properly embedded surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ A Delaunay-type classification result for prescribed mean curvature surfaces in \(\mathbb{M}^2(\kappa) \times \mathbb{R} \) ⋮ Translating solitons of the mean curvature flow in the space \(\mathbb{H}^2\times \mathbb{R}\) ⋮ Maximum principle for semi-elliptic trace operators and geometric applications ⋮ Height estimate for special Weingarten surfaces of elliptic type in 𝕄²(𝕔)×ℝ ⋮ Hypersurfaces of constant higher-order mean curvature in \(M\times{\mathbb{R}}\) ⋮ Cylindrically bounded constant mean curvature surfaces in $\mathbb {H} ^2\times \mathbb {R}$

Cites Work

• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• The structure of complete embedded surfaces with constant mean curvature
• Foliations by constant mean curvature tubes
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• Constant mean curvature surfaces in homogeneously regular 3-manifolds
• Constant Mean Curvature Surfaces in Hyperbolic Space
• Constant mean curvature surfaces in 𝑀²×𝐑
• The topology and geometry of embedded surfaces of constant mean curvature

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