Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A LIOUVILLE TYPE THEOREM FOR HARMONIC MORPHISMS

  • Jung, Seoung-Dal (DEPARTMENT OF MATHEMATICS CHEJU NATIONAL UNIVERSITY) ;
  • Liu, Huili (DEPARTMENT OF MATHEMATICS NORTHEASTERN UNIVERSITY) ;
  • Moon, Dong-Joo (DEPARTMENT OF MATHEMATICS CHEJU NATIONAL UNIVERSITY)
  • Published : 2007.07.30
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Abstract

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let ${\mu}0$ be the least eigenvalue of the Laplacian acting on $L^2-functions$ on M. We show that if $Ric^M{\ge}-{\mu}0$ at all $x{\in}M$ and either $Ric^M>-{\mu}0$ at some point x0 or Vol(M) is infinite, then every harmonic morphism ${\phi}:M{\to}N$ of finite energy is constant.

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References

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  1. LIOUVILLE TYPE THEOREM FOR p-HARMONIC MAPS II vol.29, pp.1, 2014, https://doi.org/10.4134/CKMS.2014.29.1.155
  2. Liouville type theorems for p-harmonic maps vol.342, pp.1, 2008, https://doi.org/10.1016/j.jmaa.2007.12.018