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

Qun Chen, Jürgen Jost, and Hongbing Qiu

Contact the author: Please use for correspondence this email.
Submission date: 01. Aug. 2014
Pages: 23
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
Bibtex
MSC-Numbers: 58E20, 53C27
Keywords and phrases: V-harmonic map, noncompact manifold, existence, liouville theorem, V-Laplacian comparison theorem
Download full preprint: PDF (426 kB)

Abstract:
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.