A general Schwarz lemma for Kahler manifolds

Shing-Tung Yau

Metric Geometry mathscidoc:1912.43470

American Journal of Mathematics, 100, (1), 197-203, 1978.2
Introduction. The classical Schwarz-Pick lemma states that any holomorphic map of the unit disk into itself decreases the Poincare metric. Later Ahlfors generalized this lemma to holomorphic mappings between two Riemann surfaces where curvatures of these Riemann surfaces were used in a very explicit way. More recently, Chern initiated the study of holomorphic mappings between higher-dimensional complex manifold by generalizing the Ahlfors lemma to these spaces. Then this lemma was further extended by Kobayashi, Griffiths, Wu and others. It plays a very important role in their theory. In this note, we shall prove the following generalization of the Schwarz lemma.
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@inproceedings{shing-tung1978a,
  title={A general Schwarz lemma for Kahler manifolds},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203448713276034},
  booktitle={American Journal of Mathematics},
  volume={100},
  number={1},
  pages={197-203},
  year={1978},
}
Shing-Tung Yau. A general Schwarz lemma for Kahler manifolds. 1978. Vol. 100. In American Journal of Mathematics. pp.197-203. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203448713276034.
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