The tag has no wiki summary.

learn more… | top users | synonyms

3
votes
0answers
125 views

Is there a coordinate free proof of the Morrey--Kohn--Hormander identity?

The Morrey--Kohn--Hormander identity is the key to proving vanishing/existence results on bounded pseudoconvex domains in $\mathbb{C}^n$, or more generally, Stein domains. See, for instance, the ...
1
vote
0answers
49 views

About interpolability of Stein structures

Imagine $V$ is a complex vector space and $U_1\subset U_2\subset V$ two Euclidean balls. Let $\psi,\psi_1$ be strictly plurisubharmonic functions on $V$ and $U_1$ respectively. Question: What are ...
1
vote
1answer
127 views

what's the cohomological dimension of a Stein space?

I want to know the "cohomological dimension" of a Stein manifold. I know that: for $X$ differential manifold and for every sheaf $F$ of abelian groups, I have $H_c^j(X,F)=H^j(X,F)=0$ for ...
2
votes
1answer
271 views

Cotangent bundle of coadjoint orbit is stein manifold?

Let me first define stein manifolds and coadjoint orbits. A complex manifold $X$ of complex dimension $n$ is called a Stein manifold if the following conditions hold: $X$ is holomorphically convex, ...
0
votes
1answer
450 views

Stein manifolds definiton

There are a few equivalent definitions of Stein manifolds. As far as I know they were initially defined as holomorphically convex complex manifolds, and then the other definitions (e.g. complex ...
8
votes
1answer
703 views

Question about an estimate in Hörmander's proof of Cartan's Theorem B

I have been working through the proof of Cartan's Theorem B that Hörmander gives in his book 'Introduction to Complex Analysis in Several Variables'. When I began, I skipped over some of the initial ...
2
votes
0answers
277 views

reference for p-adic Stein spaces

Hi, I'm looking for a reference in english for p-adic Stein spaces. The usual referneces I come across are all in german. Thanks
2
votes
1answer
332 views

A basic question on the definition of Cartan-Remmert reduction and holomorphic convexity

Here is a definition of holomorphic convexity taken from the notes of Eyssidieux: Defintion. A complex analytic space $S$ is holomorphically convex if there is a proper holomorphic morphism $\pi: ...
2
votes
1answer
513 views

Plurisubharmonic exhaustion functions without critical points at infinity

A complex manifold $X$ is said to be weakly pseudoconvex if there exists on $X$ a smooth plurisubharmonic exhaustion function $\psi$. For example, Stein manifolds are weakly pseudoconvex (in this ...
4
votes
1answer
208 views

Stein manifolds isomorphic at infinity

Suppose $M$ and $N$ are two Stein manifolds of dimension at least $3$ with compact subsets $U$ and $V$ such that $M\setminus U$ is biholomorphic to $N \setminus V$. It it true that $M$ is ...