Biharmonic hypersurfaces with bounded mean curvature

Abstract

We consider a complete biharmonic hypersurface with nowhere zero mean curvature vector field $\varphi :(M^m,g)\to (S^{m+1},h)$ in a sphere. If the squared norm of the second fundamental form $B$ is bounded from above by m, and ${\int }_M{H}^{-p}d{v}_g<\infty$, for some $0<p<\infty$, then the mean curvature is constant.

8 pages

References in corpus (2)

• Biharmonic Riemannian submersions from 3-manifolds
• Biharmonic submanifolds in manifolds with bounded curvature