scholarly journals A characterization of compact surfaces with constant mean curvature

1990 ◽  
Vol 108 (2) ◽  
pp. 483-483 ◽  
Author(s):  
Masaaki Umehara
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Compact Surfaces

scholarly journals Unitarization of Loop Group Representations of Fundamental Groups

2007 ◽  
Vol 187 ◽  
pp. 1-33 ◽  
Author(s):  
Josef Dorfmeister ◽  
Hongyou Wu
Keyword(s):  
Fundamental Group ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Loop Group ◽  
Fundamental Groups ◽  
Matrix Functions ◽  
Group Representations ◽  
Constant Mean Curvature Surfaces ◽  
Finite Set

AbstractIn this paper, we give a characterization of the simultaneous unitarizability of any finite set of SL(2, ℂ)-valued functions on and determine all possible ways of the unitarization. Such matrix functions can be regarded as images of the generators for the fundamental group of a surface in an -family, and the results of this paper have applications in the construction of constant mean curvature surfaces in space.

scholarly journals Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Henrique F. de Lima ◽  
Joseilson R. de Lima
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurface ◽  
De Sitter Space ◽  
De Sitter ◽  
Height Estimate ◽  
Spacelike Hypersurfaces ◽  
Hyperbolic Domains

We obtain a height estimate concerning to a compact spacelike hypersurfaceΣnimmersed with constant mean curvatureHin the anti-de Sitter spaceℍ1n+1, when its boundary∂Σis contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic spaceℍn. Our estimate depends only on the value ofHand on the geometry of∂Σ.As applications of our estimate, we obtain a characterization of hyperbolic domains ofℍ1n+1and nonexistence results in connection with such types of hypersurfaces.

scholarly journals Limit lamination theorems for H-surfaces

2019 ◽  
Vol 2019 (748) ◽  
pp. 269-296 ◽  
Author(s):  
William H. Meeks III ◽  
Giuseppe Tinaglia
Keyword(s):  
Minimal Surfaces ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Structure Theorems ◽  
Compact Surfaces ◽  
Finite Genus

AbstractIn this paper we prove some general results for constant mean curvature lamination limits of certain sequences of compact surfacesM_{n}embedded in\mathbb{R}^{3}with constant mean curvatureH_{n}and fixed finite genus, when the boundaries of these surfaces tend to infinity. Two of these theorems generalize to the non-zero constant mean curvature case, similar structure theorems by Colding and Minicozzi in [6, 8] for limits of sequences of minimal surfaces of fixed finite genus.

scholarly journals Hypersurfaces with constant mean curvature and two principal curvatures in n+1

2004 ◽  
Vol 76 (3) ◽  
pp. 489-497 ◽  
Author(s):  
Luis J. Alías ◽  
Sebastião C. de Almeida ◽  
Aldir Brasil Jr.
Keyword(s):  
Fundamental Form ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Integral Formula ◽  
Second Fundamental Form ◽  
Euclidean Sphere ◽  
Principal Curvatures ◽  
Clifford Torus ◽  
The Second Fundamental Form

In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere. In the minimal case, Perdomo (Perdomo 2004) andWang (Wang 2003) obtained an integral inequality involving the square of the norm of the second fundamental form of M, where equality holds only if M is the Clifford torus. In this paper, using the traceless second fundamental form of M, we extend the above integral formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus.

scholarly journals Surfaces of Constant Mean Curvature in Euclidean 3-space Orthogonal to a Plane along its Boundary

2002 ◽  
Vol 74 (1) ◽  
pp. 33-35 ◽  
Author(s):  
PEDRO A. HINOJOSA
Keyword(s):  
Jordan Curve ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Nonzero Mean ◽  
Compact Surfaces ◽  
Planar Jordan Curve

We consider compact surfaces with constant nonzero mean curvature whose boundary is a convex planar Jordan curve. We prove that if such a surface is orthogonal to the plane of the boundary, then it is a hemisphere.

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