Annals of Global Analysis and Geometry

, Volume 42, Issue 4, pp 565–584 | Cite as

Existence and Liouville theorems for V -harmonic maps from complete manifolds

  • Qun Chen
  • Jürgen JostEmail author
  • Hongbing Qiu


We establish existence and uniqueness theorems for V-harmonic maps from complete noncompact manifolds. This class of maps includes Hermitian harmonic maps, Weyl harmonic maps, affine harmonic maps, and Finsler harmonic maps from a Finsler manifold into a Riemannian manifold. We also obtain a Liouville type theorem for V-harmonic maps. In addition, we prove a V-Laplacian comparison theorem under the Bakry-Emery Ricci condition.


V-Harmonic map Noncompact manifold Existence Liouville theorem V-Laplacian comparison theorem 

Mathematics Subject Classification

58E20 53C27 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Department of MathematicsLeipzig UniversityLeipzigGermany

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