Biharmonic hypersurfaces in a sphere

Luo, Yong; Maeta, Shun

doi:10.1090/proc/13320

Biharmonic hypersurfaces in a sphere
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by Yong Luo and Shun Maeta

Proc. Amer. Math. Soc. 145 (2017), 3109-3116

DOI: https://doi.org/10.1090/proc/13320

Published electronically: February 28, 2017

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Abstract:

In this short paper we will survey some recent developments in the geometric theory of biharmonic submanifolds, with an emphasis on the newly discovered Liouville type theorems and applications of known Liouville type theorems in the research of the nonexistence of biharmonic submanifolds. A new Liouville type theorem for superharmonic functions on complete manifolds is proved and its applications in a kind of nonexistence of biharmonic hypersurfaces in a sphere is provided.

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