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arXiv · 1506.04476

Biharmonic hypersurfaces with bounded mean curvature

Shun Maeta
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Abstract

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

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Shun Maeta. 2015-06-15. Biharmonic hypersurfaces with bounded mean curvature. https://arxiv.org/abs/1506.04476

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