Harmonic mappings and Khler manifolds

Jrgen Jost Shing-Tung Yau

Complex Variables and Complex Analysis mathscidoc:1912.43521

Mathematische Annalen, 262, (2), 145-166
In this paper, we develop an approach to the study of compact K~ hler manifolds which admit mappings of everywhere maximal rank into quotients of polydiscs, eg into Riemann surfaces or products of them. One main tool will be a detailed study of the harmonic maps in the corresponding homotopy classes (for definition and general properties of harmonic maps between Riemannian manifolds see [3]). Starting with a result of Siu, we prove in Sect. 2 that the local level sets of the components of these mappings are analytic subvarieties of the domain. This, together with a generalization of the similarity principle of Bers and Vekua which is proved in the appendix and a residue argument, enables us to give conditions involving the Chern and K~ ihler classes of the considered manifolds, under which this harmonic map is of maximal rank everywhere and, in case domain and image have the same dimension, in
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  title={Harmonic mappings and Khler manifolds},
  author={Jrgen Jost, and Shing-Tung Yau},
  booktitle={Mathematische Annalen},
Jrgen Jost, and Shing-Tung Yau. Harmonic mappings and Khler manifolds. Vol. 262. In Mathematische Annalen. pp.145-166. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203806698004085.
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