Asian Journal of Mathematics

Volume 26 (2022)

Number 1

Comparing the Carathéodory pseudo-distance and the Kähler–Einstein distance on complete reinhardt domains

Pages: 37 – 44



Gunhee Cho (Department of Mathematics, University of California, Santa Barbara, Calif., U.S.A.)


We show that on a certain class of bounded, complete Reinhardt domains in $\mathbb{C}^n$ that enjoy a lot of symmetries, the Carathéodory pseudo-distance and the geodesic distance of the complete Kähler–Einstein metric with Ricci curvature $-1$ are different.


Carathéodory pseudo-distance, Kähler–Einstein distance of Ricci curvature $-1$, complete Reinhardt domains, application of Yau’s Schwarz lemma

2010 Mathematics Subject Classification

Primary 32Q05. Secondary 32Q20.

Received 7 June 2019

Accepted 20 August 2021

Published 30 January 2023