Kang-Hyurk Lee, Smoothly Bounded Domain with a Compact Quotient

The Wong-Rosay theorem says that a smoothly bounded domain covering a compact complex manifold is biholomorphically equivalent to the unit ball. The general methodology of this theorem is the affine rescaling method. In this talk, I will introduce the potential rescaling method, an alternative of the affine rescaling. This is a method to construct a specific potential function of the Kahler-Einstein which possesses a complete holomorphic vector field. I will also give a generalization of the Wong-Rosay theorem. This is a collaborated work with Y.-J. Choi and A. Seo.