Jisoo Byun

AUTOMORPHISMS OF THE HARTOGS TYPE DOMAINS OVER CLASSICAL SYMMETRIC DOMAINS

In this paper we completely describe the automorphism group of the Hartogs type domains over bounded classical symmetric domains by using the ball characterization theorem about noncompact automorphism groups. As an application, we give plenty of examples of non-homogeneous domains in ℂn, for which the real dimension of the automorphism group is less than n2 - 1.

Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group

We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism orbits among the domains that are not necessarily bounded. This generalizes the recent work of Kim and Krantz [6]. Key new features of this article include: a lower bound estimate of the Kobayashi metric and distance near a pluri-subharmonic peak boundary point of the domains in Banach spaces, an effective localization argument, and an improvement of weak-type convergence of sequences of biholomorphic mappings of domains in Banach spaces.