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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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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.
Kilian, Martin +2 more
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On timelike hypersurfaces of the Minkowski 4-space with 1-proper second mean curvature vector [PDF]
Journal of Mahani Mathematical Research, 2023 The mean curvature vector field of a submanifold in the Euclidean $n$-space is said to be $proper$ if it is an eigenvector of the Laplace operator $\Delta$.
Firooz Pashaie +3 more
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Stable constant mean curvature hypersurfaces [PDF]
Proceedings of the American Mathematical Society, 2007 This paper is devoted to the study of constant-mean-curvature-hypersurfaces \(M^n\) (called here \(H\)-hypersurfaces) in a Riemannian manifold \(\mathcal N^{n+1} \; (n = 3, 4)\,\) which has sectional curvature uniformly bounded from below. If \(\text{sec} (\mathcal N)\) denotes the infimum of the sectional curvatures of \(\mathcal N\) and \(H\) the ...
ELBERT F, NELLI, BARBARA, ROSENBERG H.
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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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On hypersurfaces of Lorentzian standard 4-space forms satisfying a biconservativity condition [PDF]
Journal of Mahani Mathematical Research, 2023 In this manuscript, we consider an extended version of biconservativity condition (namely, ${\textrm C}$-biconservativity) on the Riemannian hypersurfaces of Lorentzian standard 4-space forms.
Firooz Pashaie
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A Note on Constant Mean Curvature Foliations of Noncompact Riemannian Manifolds
International Journal of Mathematics and Mathematical Sciences, 2022 We aimed to study constant mean curvature foliations of noncompact Riemannian manifolds, satisfying some geometric constraints. As a byproduct, we answer a question by M. P. do Carmo (see Introduction) about the leaves of such foliations.
S. Ilias, B. Nelli, M. Soret
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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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