Comparing the Carathéodory Pseudo-Distance and the Kähler-Einstein Distance on Complete Reinhardt Domains

Abstract

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.

arXiv commentBe accepted in Asian Journal of Mathematics