Biharmonic conjectures on hypersurfaces in a space form

Fu, Yu; Hong, Min-Chun; Zhan, Xin

doi:10.1090/tran/9021

Biharmonic conjectures on hypersurfaces in a space form
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by Yu Fu, Min-Chun Hong and Xin Zhan;

Trans. Amer. Math. Soc. 376 (2023), 8411-8445

DOI: https://doi.org/10.1090/tran/9021

Published electronically: September 14, 2023

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Abstract:

We apply the Murnaghan-Nakayama rule in the representation theory of symmetric groups to develop new techniques for studying biharmonic hypersurfaces in a space form. As applications of the new techniques, we settle the well-known Chen’s conjecture on biharmonic hypersurfaces in $\Bbb R^6$ and BMO conjecture on biharmonic hypersurfaces in $\mathbb S^6$.

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