## The heat flow of $V$-harmonic maps from complete manifolds into regular balls

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## Abstract:

In this paper, we establish gradient estimates for the heat flow of $V$-harmonic maps from complete noncompact manifolds into regular balls. We also derive a Liouville theorem for $V$-harmonic maps, which improves Theorem 2 in a prior work of the author, Chen and Jost and covers the results of that work and a work of Brighton. Furthermore, using these gradient estimates, we prove the global existence for the $V$-harmonic map heat flow and generalize the result obtained by Chen-Jost-Wang to the case where the domain manifold is complete noncompact.## References

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## Additional Information

**Hongbing Qiu**- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China – and – Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany
- MR Author ID: 889513
- Email: hbqiu@whu.edu.cn
- Received by editor(s): September 1, 2015
- Received by editor(s) in revised form: June 12, 2016
- Published electronically: January 27, 2017
- Communicated by: Lei Ni
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 2271-2280 - MSC (2010): Primary 58E20, 53C43
- DOI: https://doi.org/10.1090/proc/13332
- MathSciNet review: 3611336