Abstract

Abstract In this chapter we begin our study of plurisubharmonic functions; they will play the central part throughout the remaining chapters. First, however, we present a comprehensive account of some fundamental properties of harmonic, pluriharmonic, and subharmonic functions. We also give some examples of applications of these functions in complex analysis. This is followed by a short exposition of some fundamental properties of plurisubharmonic functions. The analogies between plurisubharmonicity, pseudoconvexity, and convexity (of functions and sets, respectively) are explored in the exercises closing the chapter.

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