1. The core of a complex manifold- Part I We introduce the core of a complex manifold, 

and we discuss questions and results related to analytic structure and Liouville 

type properties of the core.

2. The core of a complex manifold- Part II We formulate sufficient conditions for the 

existence of the Bergman metric on unbounded pseudoconvex domains, and we dicuss core

sets with respect to families of plurisubharmonic functions of different smoothness classes