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Given a Stein manifold $Y$, there exists $\rho$, a $\mathscr C^2$-smooth strictly plurisubharmonic exhausting function for $Y$, such that the set of critical points $C=\{z\in Y\;:\;d\rho(z)=0\}$ is ...

Let $Z\subset \mathbb{C}^n$ a domain of holomorphy with smooth boundary $\partial Z$ and closure $\bar Z$. There is a natural notion of holomorphic vector bundle over $\bar Z$, given in terms of ...

I am reading this article by Bingyuan Liu on the Diederich-Fornæss index. I am having some problems with both the notation and the geometrical side. 1)I don't know what kind of objects $N,L$ are ...

From this MSE question and its answer, and from this MO question I have learned of the following remarkable theorem of Wolfgang Fischer and Hans Grauert. Theorem. A proper holomorphic submersion with ...

There are many theorems which now could be called "The Ohsawa-Takegoshi" theorem. Of these, the most basic is roughly the following: Let $\Omega \subset \subset \mathbb{C}^n$ be a psuedoconvex ...