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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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$V$-harmonic morphisms between Riemannian manifolds
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by Guangwen Zhao PDF
Proc. Amer. Math. Soc. 148 (2020), 1351-1361 Request permission

Abstract:

A $V$-harmonic morphism $u:M\to N$ between Riemannian manifolds is a smooth map which pulls back germs of harmonic functions on $N$ to germs of $V$-harmonic functions on $M$, where $V$ is a smooth vector field on $M$. In this paper, we give some characterizations and examples of $V$-harmonic morphisms. In addition, a dilation estimate and a Liouville-type theorem of $V$-harmonic morphisms from noncompact complete manifolds are also established. As applications, we obtain the Liouville-type theorems for $V$-harmonic morphisms from complete manifolds of nonnegative Bakry-Émery Ricci curvature, especially complete steady or shrinking Ricci solitons, to manifolds of dimension at least three or compact Riemann surface of genus at least two.
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Additional Information
  • Guangwen Zhao
  • Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
  • MR Author ID: 1238820
  • Email: gwzhao@fudan.edu.cn
  • Received by editor(s): May 26, 2019
  • Received by editor(s) in revised form: July 22, 2019
  • Published electronically: November 4, 2019
  • Communicated by: Guofang Wei
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 1351-1361
  • MSC (2010): Primary 58E20, 53C43; Secondary 32Q60, 35B53
  • DOI: https://doi.org/10.1090/proc/14811
  • MathSciNet review: 4055960