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Constant mean curvature surfaces [PDF]
Surveys in Differential Geometry, 2016 In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of Riemannian $n$-manifolds.
H. Meeks III, William +2 more
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Index and Total Curvature of Surfaces with Constant Mean Curvature [PDF]
Proceedings of the American Mathematical Society, 1990 We prove an analogue, for surfaces with constant mean curvature in hyperbolic space, of a theorem of Fischer-Colbrie and Gulliver about minimal surfaces in Euclidean space. That is, for a complete surface
Manfredo P. do Carmo +1 more
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Constant Mean Curvature Surfaces for the Bessel Equation [PDF]
Springer Proceedings in Mathematics and Statistics, 2021 In this note we construct a family of immersions with constant mean curvature of the twice-punctured Riemann sphere into R^3 from the Bessel equation.
exaly +3 more sources
Examples of surfaces of constant mean curvature
Дифференциальная геометрия многообразий фигур, 2019 A surface in E3 is called parallel to the surface M if it consists of the ends of constant length segments, laid on the normals to the surfaces at points of this surface. The tangent planes at the corresponding points will be parallel.
M. A. Cheshkova
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Constant Mean Curvature Surfaces Along a Spacelike Curve
Cumhuriyet Science Journal, 2022 We construct constant mean curvature surfaces along a given spacelike curve in 3 dimensional Minkowski space. We parametrically present these surfaces using the famous Frenet frame of the curve in question.
Ergin Bayram
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New Constant Mean Curvature Surfaces [PDF]
Experimental Mathematics, 2000 We use the Dorfmeister–Pedit–Wu construction to present three new classesof immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic.
Martin Kilian +2 more
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Constant mean curvature surfaces in AdS 3 [PDF]
Journal of High Energy Physics, 2010 19 pages, v2: minor corrections, to appear in ...
Sakai, Kazuhiro, Satoh, Yuji
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Stability of helicoidal surfaces with constant mean curvature
International Journal of Mathematics for Industry, 2020 Motivated by an experimental result on the shape of liquid water supported by a small stainless helical wire, we find a class of stable helicoidal convex surfaces with constant mean curvature whose boundary consists of a single helix and two short arcs.
Yuta Hatakeyama, Miyuki Koiso
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Simons type formulas for surfaces in Sol3 and applications
Bulletin of Mathematical Sciences, 2023 We compute the Laplacian of the squared norm of the second fundamental form of a surface in Sol3 and then use this Simons type formula to obtain some gap results for compact constant mean curvature surfaces of this space.
Dorel Fetcu
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On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group
Journal of New Theory, 2022 This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group.
Sevinç Taze, Zuhal Kucukarslan Yuzbasi
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