A SURVEY OF PLURISUBHARMONIC FUNCTIONS

Çiğdem Çelik
Mathematics, MSc. Thesis, 2015

Thesis Jury

Prof. Dr. Aydın Aytuna (Thesis Advisor),  Prof. Dr. Vyacheslav Zakharyuta, Assoc. Prof. Dr. Mert Çağlar

Date &Time: 5th January, 2015 –  13:00

Place: L062

Keywords : Subharmonic function, plurisubharmonic function, Dirichlet problem,

pluripolar set, extremal function, pluricomplex Green function.

Abstract

Plurisubharmonic functions have been introduced by Lelong and Oka in 1942. These functions play a major role in the theory of several complex variables.

In this thesis, we present a survey of plurisubharmonic functions as one of the generalizations of subharmonic functions in one complex variable. Thereby, in the first part of this study, we recall the main definitions and theorems of subharmonic functions. In the rest parts, we focus on multidimensional case and aim to give main principles of the theory of plurisubharmonic functions.