Young-jun Choi, Existence of a Complete Holomorphic Vector Field via the Kähler-Einstein Metric

A fundamental problem in Several Complex Variables is to classify bounded pseudoconvex domains in the complex Euclidean space with a noncompact automorphism group, especially with a compact quotient. In the results of Wong-Rosay and Frankel, they make use of the “Scaling method” for obtaining an 1-parameter family of automorphisms, which generates a holomorphic vector field.

In this talk, we discuss the existence of a nowhere vanishing complete holomorphic vector field on a strongly pseudoconvex manifold admitting a negatively curved Kähler-Einstein metric and discrete sequence of automorphisms by introducing the scaling method on potentials of the Kähler-Einstein metric.

This is a joint work with Kang-Hyurk Lee in Gyenongsang National University.