Biharmonic hypersurfaces in hemispheres

Abstract

In this paper we consider the Balmuş-Montaldo-Oniciuc's conjecture in the case of hemispheres. We prove that a compact non-minimal biharmonic hypersurface in a hemisphere of $S^{n+1}$ must be the small hypersphere $S^n\left(1/\sqrt{2}\right)$, provided that $n^2-H^2$ does not change sign.

9 pages