Some regularity properties of the Azukawa pseudometric for a wide class of domains (including bounded hyperconvex domains) are proven. Among others we prove that in this class of domains the Azukawa metric is continuous and the upper limit in its definition may be replaced with the limit. Some properties of the pluricomplex Green function with one (as well as with many) pole are also given.
Włodzimierz ZWONEK. "Regularity properties of the Azukawa metric." J. Math. Soc. Japan 52 (4) 899 - 914, October, 2000. https://doi.org/10.2969/jmsj/05240899