Existence and Liouville theorems for V-harmonic maps from complete manifolds
Qun Chen, Jürgen Jost, and Hongbing Qiu
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Submission date: 01. Aug. 2014
published in: Annals of global analysis and geometry, 42 (2012) 4, p. 565-584
DOI number (of the published article): 10.1007/s10455-012-9327-z
MSC-Numbers: 58E20, 53C27
Keywords and phrases: V-harmonic map, noncompact manifold, existence, liouville theorem, V-Laplacian comparison theorem
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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 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.