Complete hypersurfaces in Euclidean spaces with vanishing r-mean curvatures
Maria Fernanda Elbert | Carmo, Manfredo do
Topology | r-mean curvature | finite total curvature | complete | stability.
Hypersurfaces in euclidean spaces with vanishing r-mean curvatures are natural generalizations of minimal hypersurfaces. When they are complete and have finite total curvature, we prove that their topological structure is similar to that of minimal hypersurfaces. We apply this result to prove a theorem on stability, a gap theorem on the total curvature, and a non-existence theorem for one-ended hypersurfaces with even dimensions.