Biharmonic hypersurfaces with bounded mean curvature

Maeta, Shun

doi:10.1090/proc/13335

Biharmonic hypersurfaces with bounded mean curvature
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Proc. Amer. Math. Soc. 145 (2017), 1773-1779 Request permission

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. This is an affirmative partial answer to the BMO conjecture for biharmonic submanifolds.

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