Bergman Kernel in Complex Analysis

Abstract

In this survey a brief review of results on the Bergman kernel and Bergman distance concentrating on those fields of complex analysis which remain in the focus of the research interest of the authors is presented. The topics discussed contain general discussion of L 2 h spaces, behavior of the Bergman distance, regularity of extension of proper holomorphic mappings, and recent development in the theory of Bergman distance stemming from the pluripotential theory and very short discussion of the Lu Qi Keng problem.