scholarly journals Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve

2021 ◽  
Author(s):  
Ergin BAYRAM
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Timelike Curve

Non-lightlike ruled surfaces with constant curvatures in Minkowski 3-space

2018 ◽  
Vol 15 (04) ◽  
pp. 1850068 ◽  
Author(s):  
Ahmad Tawfik Ali
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Ruled Surface ◽  
Timelike Curve ◽  
Ruled Surfaces ◽  
Base Curve ◽  
Timelike Ruled Surface ◽  
Interesting Theorem

We study the non-lightlike ruled surfaces in Minkowski 3-space with non-lightlike base curve [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] are the tangent, principal normal and binormal vectors of an arbitrary timelike curve [Formula: see text]. Some important results of flat, minimal, II-minimal and II-flat non-lightlike ruled surfaces are studied. Finally, the following interesting theorem is proved: the only non-zero constant mean curvature (CMC) non-lightlike ruled surface is developable timelike ruled surface generated by binormal vector.

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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