Biharmonic hypersurfaces in hemispheres

Matheus Vieira

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arXiv · 2008.08274

Biharmonic hypersurfaces in hemispheres

Matheus Vieira

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Abstract

In this paper we consider the Balmu\c{s}-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.

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Matheus Vieira. 2020-08-19. Biharmonic hypersurfaces in hemispheres. https://arxiv.org/abs/2008.08274

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