Rothstein (1955) first introduced pseudoconvexity using generalized Hartogs figures. Słodkowski (1986) defined pseudoconvex sets by means of the existence of exhaustion functions which are plurisubharmonic in the sense of Hunt and Murray (1978). Examples of pseudoconvex sets appear as complements of  analytic sets. Here, the relation of the analytic structure of graphs of continuous surfaces whose complements are pseudoconvex is investigated. As an outcome, the authors generalize results by Hartogs (1909), Shcherbina (1993), and Chirka (2001) on the existence of foliations of pseudoconcave continuous real hypersurfaces by smooth complex ones.  weiterlesen