Could anyone help me find the difference between strictly and strongly pseudoconvex domains in $\mathbb{C}^n$? I managed to find in the literature only the definition of strictly pseudoconvex domains (e.g. in "The Cauchy Riemann complex" page 74 or in "holomorphic functions and integral representation in several complex variables" page 59) as domains $\Omega\subset\mathbb{C}^n$ which admit a plurisubharmonic defining function.
However, I cannot find a definition of strongly pseudoconvex domains, but it seems to me that these terms are used interchangeably. Summarizing:
- Where can I find a proper definition of strongly pseudoconvex domains?
- Which is the difference between the notions of strictly and strongly pseudoconvex domains?
Any help is appreciated!
In my experience, "strictly pseudoconvex" and "strongly pseudoconvex" are synonymous; I've never seen anyone make a distinction between them. They both mean that the Levi form is positive definite at all points of $\partial \Omega$. One source for the definition is Steve Krantz's Function Theory of Several Complex Variables (he calls it "strictly Levi pseudoconvex"); but I'm sure there are many others.