Annals of Global Analysis and Geometry

, Volume 46, Issue 3, pp 259–279 | Cite as

Omori–Yau maximum principles, \(V\)-harmonic maps and their geometric applications

  • Qun Chen
  • Jürgen JostEmail author
  • Hongbing Qiu


We establish a V-Laplacian comparison theorem under the Bakry–Emery Ricci condition and then give various Omori–Yau type maximum principles on complete noncompact manifolds. We also obtain Liouville theorems for V-harmonic maps. We apply these findings to Ricci solitons and self-shrinkers.


Omori–Yau maximum principle V-Laplacian V-harmonic map Ricci soliton Self-shrinker 

Mathematics Subject Classification (2000)

58E20 53C27 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

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

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