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### Homology 3-sphere with a unique Stein-fillable contact structure

Are there any known examples of oriented integer homology 3-spheres $Y$ (besides $S^3$) which have exactly one Stein-fillable contact structure up to isotopy? Failing that, what are the known examples ...
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### Trivialisation of vector bundles on Stein spaces

Does every vector bundle on a Stein space have a finite local trivialisation? Definitions: Stein space means either a complex analytic Stein space or a nonarchimedean Stein space in the sense of ...
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### 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 ...
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### 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 ...
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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 $j>\... 1answer 374 views ### Cotangent bundle of coadjoint orbit is stein manifold? Let me first define stein manifolds and coadjoint orbits. A complex manifold$X$of complex dimension$n$is called a Stein manifold if the following conditions hold:$X$is holomorphically convex, ... 1answer 699 views ### Stein manifolds definiton There are a few equivalent definitions of Stein manifolds. As far as I know they were initially defined as holomorphically convex complex manifolds, and then the other definitions (e.g. complex ... 1answer 748 views ### Question about an estimate in Hörmander's proof of Cartan's Theorem B I have been working through the proof of Cartan's Theorem B that Hörmander gives in his book 'Introduction to Complex Analysis in Several Variables'. When I began, I skipped over some of the initial ... 0answers 321 views ### reference for p-adic Stein spaces Hi, I'm looking for a reference in english for p-adic Stein spaces. The usual referneces I come across are all in german. Thanks 1answer 390 views ### A basic question on the definition of Cartan-Remmert reduction and holomorphic convexity Here is a definition of holomorphic convexity taken from the notes of Eyssidieux: Defintion. A complex analytic space$S$is holomorphically convex if there is a proper holomorphic morphism$\pi: S\...
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 ...
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 ...