Characterizations of some domains via Carathéodory extremals (1802.09067v2)

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 Carath\'eodory extremal problems in the domain.