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

This work is a survey of the properties of q-pseudoconvex and q-holomorphically convex domains in CN, 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 q̃-pseudoconvexity of the complement of q-pseudoconvex sets.