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Constant mean curvature surfaces of any positive genus [PDF]
, 2023 The paper shows the existence of several new families of noncompact constant mean curvature surfaces: (i) singly punctured surfaces of arbitrary genus g 1, (ii) doubly punctured tori, and (iii) doubly periodic surfaces with Delaunay ...
Kobayashi, S.-P. +3 more
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Superharmonicity of curvatures for surfaces of constant mean curvature [PDF]
Pacific Journal of Mathematics, 1992 The article deals with the superharmonicity of some curvatures (the scalar curvature \(R\), the Gauss-Kronecker curvature \(K\), the \(\nu\)-th mean curvature \({K}_ \nu\), the level curvature \(L\)) of hypersurfaces of constant mean curvature in \(\mathbb{R}^ n\). For instance, it is proved that for a hypersurface of positive sectional curvatures \(R\)
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The PDE describing constant mean curvature surfaces [PDF]
, 2001 summary:We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential ...
Wu, Hongyou
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Constant mean curvature surfaces on a strip [PDF]
Pacific Journal of Mathematics, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Constant mean curvature surfaces with circular boundary in R³
Anais da Academia Brasileira de Ciências, 2006 In this work we deal with surfaces immersed in R³ with constant mean curvature and circular boundary. We improve some global estimates for area and volume of such immersions obtained by other authors.
Pedro A. Hinojosa
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Stability of surfaces with constant mean curvature [PDF]
Proceedings of the American Mathematical Society, 1989 The notion of stability for surfaces with constant mean curvature H used in this paper is not the appropriate one. It requires the second variation of area to be positive for all compactly supported variations, and not only for those that preserve volume. This is such a strong definition that with it round spheres are not stable [cf. \textit{J.
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Constant Mean Curvature Spacelike Surfaces in Lorentzian Warped Products
Advances in Mathematical Physics, 2015 We characterize the spacelike slices of a Lorentzian warped product as the only constant mean curvature spacelike surfaces under suitable geometrical and physical assumptions.
Juan A. Aledo, Rafael M. Rubio
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Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
Anais da Academia Brasileira de Ciências, 2002 In this note we present a method for constructing constant mean curvature on surfaces in hyperbolic 3-space in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the ...
LEVI L. DE LIMA, PEDRO ROITMAN
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Delaunay ends of constant mean curvature surfaces [PDF]
Compositio Mathematica, 2008 Abstract The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation (ODE) with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean
Kilian, Martin +2 more
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On curvature estimates for constant mean curvature surfaces [PDF]
, 2012 In this paper we review four curvature estimates for constant mean curvature surfaces in R-3. They are the Schoen Curvature Estimate, the Choi-Schoen Curvature Estimate, the One-sided Curvature Estimate by Colding and Minicozzi and the Curvature Estimate
Tinaglia, Giuseppe; id_orcid +1 more
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