The influence of the boundary behaviour on hypersurfaces with constant mean curvature in Hn+1.

This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.

Hypersurfaces with constant inner curvature of the second fundamental form, and the non-rigidity of the sphere.

Wolfgang Kühnel, Markus Becker (1996)

Mathematische Zeitschrift

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Entire Spacelike Hypersurfaces on Constant Mean Curvature in Minkowski Space.

Andrejs E. Treibergs (1982)

Inventiones mathematicae

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Complete hypersurfaces with constant scalar curvature in a sphere

Ximin Liu, Hongxia Li (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, by using Cheng-Yau’s self-adjoint operator $□$ , we study the complete hypersurfaces in a sphere with constant scalar curvature.

Comparison principles for hypersurfaces of prescribed mean curvature.

Klaus Steffen, Frank Duzaar (1994)

Journal für die reine und angewandte Mathematik

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