A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry

Qun Chen, Jürgen Jost, and Guofang Wang

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Submission date: 16. Jul. 2014
Pages: 20
published in: The journal of geometric analysis, 25 (2015) 4, p. 2407-2426 
DOI number (of the published article): 10.1007/s12220-014-9519-9
Bibtex
MSC-Numbers: 58J05, 53C43, 35J47
Keywords and phrases: V-harmonic map, maximum principle, uniqueness, existence
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Abstract:
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 [?], Weyl harmonic maps [?], affine harmonic maps [?] 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.