On convex hulls and pseudoconvex domains generated by -plurisubharmonic functions, part I

This work is a survey of the properties of q -pseudoconvex and q -holomorphically convex domains in C N , which are defined by hulls with respect to the q -plurisubharmonic and q -holomorphic functions. We give a list of the basic properties of this type of functions and domains and the relations to each other. We also check for the q ̃ -pseudoconvexity of the complement of q -pseudoconvex sets.