## Bôcher-type theorem on n-dimensional manifolds with conical metric

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- by Jiayu Li and Fangshu Wan PDF
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**147**(2019), 4527-4538 Request permission

## Abstract:

We generalize the Bôcher-type theorem and give a sharp characterization of the behavior at the isolated singularities of a solution bounded on one side for the equation $\Delta _g u =0$ on singular manifolds with conical metrics. Furthermore, we also obtain a Liouville-type result which demonstrates that the fundamental solution is the unique nontrivial solution of $\operatorname {div}(|x|^\theta \nabla u)=0$ in $\mathbb {R}^n\setminus \{0\}$ that is bounded on one side in both a neighborhood of the origin as well as at infinity.## References

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## Additional Information

**Jiayu Li**- Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, AMSS CAS, Beijing 100190, People’s Republic of China
- MR Author ID: 274510
- Email: jiayuli@@ustc.edu.cn
**Fangshu Wan**- Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, People’s Republic of China
- MR Author ID: 1179231
- Email: wfangshu@@mail.ustc.edu.cn
- Received by editor(s): October 4, 2018
- Received by editor(s) in revised form: January 20, 2019
- Published electronically: June 27, 2019
- Additional Notes: The work was supported by NSFC, No. 11721101.
- Communicated by: Guofang Wei
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4527-4538 - MSC (2010): Primary 58J05; Secondary 35J15
- DOI: https://doi.org/10.1090/proc/14554
- MathSciNet review: 4002561