Can anyone recommend me a book on pluripotential theory with an intuitive approach? I have some course notes on that subject, but it's really abstract and theoretical. I want to understand why pluripotential/subharmonic/... were introduced and so on. My teacher wanted us to learn the book's Z.Blocki...
Ex: I don't understand :(
1/ Suppose that $u: \Omega \to \mathbb{R} $, a function $u$ is called harmonic if $u$ is continouns and $$u(x_0)=\dfrac{1}{V_n(B(x_0,r))}\int_{B(x_0,r)}u(x)\mathrm{d}V_n(x)$$.
2/ We have $u(x_0)=\dfrac{1}{\sigma(\partial B(x_0,r))}\int_{\partial B(x_0,r)}u(x)\mathrm{d}\sigma(x)$.
Your comments & suggestions are ALWAYS appreciated.
First of all, I don't think you will be able to find something really "intuitive". Pluripotential theory is rather theoretical and also a highly specialist field. You should already have a solid background in classical potential theory and measure theory before you attempt to learn pluripotential theory.
A very good introduction to classical potential theory is
That said, I would suggest that you start with the material in
It only covers the very basics, but is very readable and a gentle introduction.
For more throrough treatments, have a look at
Klimek, Pluripotential theory. This was the first book published on the subject and is a little dated.
The lecture notes by Błocki are very good.
I haven't read them myself, but the lecture notes by Bracci and Trapani also look good.
There is also a lot of material on pluripotential theory in Demailly's excellent book on complex analytic methods in algebraic geometry.
It may also be a good idea to read some of the old original research papers, for example I recommend
E. Bedford, B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation. Invent. Math. 37 (1976), 1-44.
J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables. Trans. Amer. Math. Soc. 105 (1962), 322-357.
J. Siciak, Extremal plurisubharmonic functions, Ann. Pol. Math. 39 (1981), 175-211.
There are lots of other papers I could recommend if I know what particular areas you are interested in.