Displaying similar documents to “Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups”

On minimal homothetical hypersurfaces

Lin Jiu, Huafei Sun (2007)

Colloquium Mathematicae

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We give a classification of minimal homothetical hypersurfaces in an (n+1)-dimensional Euclidean space. In fact, when n ≥ 3, a minimal homothetical hypersurface is a hyperplane, a quadratic cone, a cylinder on a quadratic cone or a cylinder on a helicoid.

On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)

Commentationes Mathematicae Universitatis Carolinae

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Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is...

Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product

Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Jr. Lima, Adriano A. Medeiros (2017)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.

Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

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We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.