Half-space theorems for mean curvature one surfaces in hyperbolic space

DOI10.1090/S0002-9939-98-04510-9zbMath0904.53041OpenAlexW1786780762MaRDI QIDQ4211004

Harold Rosenberg, Lucio L. Rodriguez

Publication date: 10 September 1998

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-98-04510-9

zbMATH Keywords

horospheresconstant mean curvature surfacehyperbolic 3-spacegeneralizations of the halfspace theorem for minimal 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 (12)

Some half-space theorems in the real projective space ⋮ Generalized Weingarten surfaces of harmonic type in hyperbolic 3-space ⋮ 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 \(\mathbb{H}^{2}\times\mathbb{R}\) ⋮ \(p\)-capacity and \(p\)-hyperbolicity of submanifolds ⋮ Half-space type theorems in warped product spaces with one-dimensional factor ⋮ 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 ⋮ The topology of large H-surfaces bounded by a convex curve ⋮ Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space ⋮ Conformal type of ends of revolution in space forms of constant sectional curvature

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