Characterizations of some domains via Carathéodory extremals

Abstract

In this paper we characterize the unit disc, the bidisc and the symmetrized bidisc \[ G =\{(z+w,zw):|z|<1,\ |w|<1\} \] in terms of the possession of small classes of analytic maps into the unit disc that suffice to solve all Carathéodory extremal problems in the domain.

to appear in the Journal of Geometric Analysis, this is the revised version after a referee's report, 17 pages