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A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry
Qun Chen, Jürgen Jost and Guofang Wang
In this note we prove that the maximum principle of Jäger-Kaul for harmonic maps holds for a more general class of maps, $V$-harmonic maps. This includes Hermitian harmonic maps [JY], Weyl harmonic maps [Kokarev], affine harmonic maps [JS] and Finsler maps from a Finsler manifold into a Riemannian manifold. With this maximum principle we establish the existence of $V$-harmonic maps into regular balls.