r-minimal hypersurfaces in space forms

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essent...

A NEW CHARACTERIZATION OF r-STABLE HYPERSURFACES IN SPACE FORMS

In this paper we study the r-stability of closed hypersurfaces with constant r-th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the r-stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the r-th mean curvature.

Hypersurfaces of Constant Curvature in Space Forms

In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where curvature means one of the symmetric functions of curvature associated to the second fundamental form. The values of the constant will be chosen so that the linearized equation will be an elliptic equation onM . For example, for surfaces in 3 the two possible curvatures are the mean curvature H and the Ga...

Rigidity Results for Hypersurfaces in Space Forms

Biharmonic Hypersurfaces in 4-dimensional Space Forms

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.