Affine translation surfaces with constant mean curvature in Euclidean 3-space

2016 ◽  
Vol 108 (2) ◽  
pp. 423-428 ◽  
Author(s):  
Huili Liu ◽  
Seoung Dal Jung
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Translation Surfaces ◽  
Affine Translation

Weighted minimal affine translation surfaces in Euclidean space with density

2018 ◽  
Vol 15 (11) ◽  
pp. 1850196 ◽  
Author(s):  
Dae Won Yoon ◽  
Zühal Küçükarslan Yüzbaşı
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Translation Surfaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Surfaces In Euclidean Space ◽  
Affine Translation

The aim of this work is to study affine translation surfaces in the Euclidean 3-space with density. We completely classify affine translation surfaces with zero weighted mean curvature.

scholarly journals On far-outlying constant mean curvature spheres in asymptotically flat Riemannian 3-manifolds

2020 ◽  
Vol 2020 (767) ◽  
pp. 161-191
Author(s):  
Otis Chodosh ◽  
Michael Eichmair
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Existence Results ◽  
Asymptotically Flat ◽  
Weingarten Surfaces ◽  
Differential Geom

AbstractWe extend the Lyapunov–Schmidt analysis of outlying stable constant mean curvature spheres in the work of S. Brendle and the second-named author [S. Brendle and M. Eichmair, Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94 2013, 3, 387–407] to the “far-off-center” regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable constant mean curvature spheres that depend delicately on the behavior of scalar curvature at infinity.

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

2011 ◽  
Vol 151 (2) ◽  
pp. 271-282 ◽  
Author(s):  
ALMA L. ALBUJER ◽  
FERNANDA E. C. CAMARGO ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Rigidity Results ◽  
Complete Spacelike Hypersurfaces ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

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