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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The heat flow of $V$-harmonic maps from complete manifolds into regular balls
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by Hongbing Qiu PDF
Proc. Amer. Math. Soc. 145 (2017), 2271-2280 Request permission

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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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