Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings Between Kähler Manifolds

We derive some consequences of the Liouville theorem for plurisubharmonic functions L.-F. Tam and author. The first result provides a nonlinear version complex splitting (which splits off factor ℂ isometrically from simply connected Kähler manifold with nonnegative bisectional curvature linear growth holomorphic function) second set results concerns so-called k-hyperbolicity its connection negativity k-scalar (when k = 1 they are sectional Kobayashi hyperbolicity) introduced recently in [33] by F. Zheng lastly prove new Schwarz-lemma-type estimate terms only curvatures both domain target manifolds. © 2020 Wiley Periodicals LLC.