# Biharmonic hypersurfaces in hemispheres

@article{Vieira2020BiharmonicHI, title={Biharmonic hypersurfaces in hemispheres}, author={Matheus Vieira}, journal={arXiv: Differential Geometry}, year={2020} }

In this paper, we consider the Balmus-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 $S^{n}\left(\frac{1}{\sqrt{2}}\right)$, provided that $n^{2}-H^{2}$ does not change sign.

## 3 Citations

Remarks on biharmonic hypersurfaces in space forms

- MathematicsDifferential Geometry and its Applications
- 2021

We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula…

Bi-eigenfunctions and biharmonic submanifolds in a sphere

- Mathematics
- 2021

In this note, we classify biharmonic submanifolds in a sphere defined by bieigenmaps (∆φ = λφ) or buckling eigenmaps (∆φ = −μ∆φ). The results can be viewed as generalizations of Takahashi’s…

Biharmonic and biconservative hypersurfaces in space forms

- Mathematics
- 2020

We present some general properties of biharmonic and biconservative submanifolds and then survey recent results on such hypersurfaces in space forms. We also propose an alternative version for a…

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