arXiv subjects
Publications and source records attributed to Wagner Oliveira Costa-Filho.
We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms.
In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r$-minimal hypersurfaces.