## Biharmonic hypersurfaces in a sphere

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- by Yong Luo and Shun Maeta PDF
- Proc. Amer. Math. Soc.
**145**(2017), 3109-3116 Request permission

## 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.## References

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## Additional Information

**Yong Luo**- Affiliation: School of mathematics and statistics, Wuhan university, Wuhan 430072, People’s Republic of China — and — Max-planck institut für mathematik In den naturwissenschaft Inselstr.22, D-04103, Leipzig, Germany
- MR Author ID: 983847
- Email: yongluo@whu.edu.cn, yongluo@mis.mpg.de
**Shun Maeta**- Affiliation: Department of Mathematics, Shimane University, Nishikawatsu 1060 Matsue, 690-8504, Japan
- MR Author ID: 963097
- Email: shun.maeta@gmail.com, maeta@riko.shimane-u.ac.jp
- Received by editor(s): November 2, 2015
- Received by editor(s) in revised form: May 23, 2016
- Published electronically: February 28, 2017
- Additional Notes: The first author was partially supported by the Postdoctoral Science Foundation of China (No. 2015M570660) and the Project-sponsored by SRF for ROCS, SEM

The second author was partially supported by the Grant-in-Aid for Young Scientists(B), No. 15K17542, Japan Society for the Promotion of Science. - Communicated by: Ken Ono
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 3109-3116 - MSC (2010): Primary 53C43; Secondary 58E20, 53C40
- DOI: https://doi.org/10.1090/proc/13320
- MathSciNet review: 3637957