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


Author: Hongbing Qiu
Journal: Proc. Amer. Math. Soc. 145 (2017), 2271-2280
MSC (2010): Primary 58E20, 53C43
DOI: https://doi.org/10.1090/proc/13332
Published electronically: January 27, 2017
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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.


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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
Email: hbqiu@whu.edu.cn

DOI: https://doi.org/10.1090/proc/13332
Keywords: $V$-harmonic maps, heat flow, gradient estimate, Liouville theorem, global existence
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
Article copyright: © Copyright 2017 American Mathematical Society