Asian Journal of Mathematics

Volume 27 (2023)

Number 1

The Schwarz lemma in Kähler and non-Kähler geometry

Pages: 121 – 134



Kyle Broder (Mathematical Sciences Institute, Australian National University, Acton, ACT, Australia; and BICMR, Peking University, Beijing, China)


We introduce a new curvature constraint that provides an analog of the real bisectional curvature considered by Yang–Zheng [28] for the Aubin–Yau inequality. A unified perspective of the various forms of the Schwarz lemma is given, leading to novel Schwarz-type inequalities in both the Kähler and Hermitian categories.


Schwarz lemma, Wu–Yau theorem, Hermitian manifolds, real bisectional curvature, holomorphic sectional curvature Schwarz bisectional curvature, partially Kähler-like metrics

2010 Mathematics Subject Classification

32Q05, 32Q20, 32Q25

The author was partially supported by an Australian Government Research Training Program (RTP) Scholarship and funding from the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (project DP220102530).

Received 22 October 2021

Accepted 21 December 2022

Published 16 June 2023