Journal of the
Korean Mathematical Society JKMS

It is well-known that there is no analogue to the Riemann mapping theorem in the higher dimensional case. Therefore, it would be an interesting question to find sufficient conditions for domains to be biholomorphically equivalent to the unit ball. In this paper, we investigate this question in the case where the given domains are generalized complex ellipsoids with spherical boundary points.

Keywords: Riemann mapping theorem, Generalized complex ellipsoids, spherical boundary points

MSC numbers: Primary 32A07; Secondary 32D15