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On complete constant mean curvature vertical multigraphs in E(κ,τ)
multigraphs constant mean curvature homogeneous spaces
2012/6/29
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
The Yamabe constant on noncompact manifolds
The Yamabe constant noncompact manifolds Differential Geometry
2012/6/19
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the ...
Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds
Caccioppoli’s inequality Simons’ equation constant mean curvature hypersurfaces stable finite index
2011/9/14
Abstract: We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, non compact, finite index, constant mean curvature hypersurface of a Riemannian ...
Gauss maps of constant mean curvature surfaces in three-dimensional homogeneous spaces
Gauss maps of constant mean curvature surfaces three-dimensional homogeneous spaces
2010/11/26
It is well-known that for a surface in a 3-dimensional real space form the constancy of
the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true
in general for...
In this paper we study constant angle surfaces in Euclidean 3--space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach...
Some Characterization of Curves of Constant Breadth in En Space
Curvature Constant Breadth Integral Characterization of Curve
2010/3/1
In this paper, the concepts concerning the space of constant breadth were extended to En-space. An approximate solution of the equation system which belongs to this curve was obtained. Using this solu...
In this paper, the concepts concerning the space curves of constant breadth were extended to E4 -space. The integral of third curvature of the curve was obtained as (bak) sds = 2k7p(k E Z) . In additi...