Abstract.
We show equality between the pluricomplex Green function (respectively, the Azukawa pseudometric) and the singular Carathéodory function (respectively, the singular Carathéodory pseudometric) for a wide class of planar domains. We also give a description of the Azukawa pseudometric of any domain in ℂn in the sense of Poletsky. All extremal discs for the Green function of any planar domain are also found. They are expressed in terms of its universal cover and Blaschke products.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
The second-named author was supported by the KBN grant no. 5 P03A 033 21.
Rights and permissions
About this article
Cite this article
Nikolov, N., Zwonek, W. Some Remarks on the Green Function and the Azukawa Pseudometric. Monatsh. Math. 142, 341–350 (2004). https://doi.org/10.1007/s00605-003-0059-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-003-0059-9