S-parabolic manifolds

Abstract

A Stein manifold is called S-Parabolic in case there exits a special plurisubharmonic exhaustion function that is maximal outside a compact set. If a continuous special plurisubharmonic exits then we will call the manifold S*-Parabolic: In one dimensional case these notions are equivalent. However in several variables the question as to weather these notions coincide seems open. In this note we establish an interrelation between these two notions.