All Questions
Tagged with reference-request several-complex-variables
12 questions with no upvoted or accepted answers
3
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Schwartz's theorem without English language reference
I'm reading the paper "Spectral Synthesis And The Pompeiu Problem" by Leon Brown, Bertram M. Schreiber and B. Alan Taylor,
Annales de l’Institut Fourier 23, No. 3, 125-154 (1973), MR352492, ...
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3
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102
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What domains are there other than unit ball and polydisc, on which Caratheodory metric is known?
What are few (bounded)domains in $\mathbb{C}^n$ on which the explicit expression of Caratheodory metric is known. For example, unit ball and unit polydisc.
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3
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637
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English reference for Fischer-Grauert theorem and its generalization by Schuster
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 ...
- 10.5k
3
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89
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Trace of a weighted composition operator on Bergman space
I am reading a series of papers by Pollicott, Jenkinson and coauthors which make use of the following type of result:
Theorem: Let $\mathbb{D} \subset \mathbb{C}^d$ be a bounded, connected open set. ...
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2
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62
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Geometric meaning of Catlin multi types
Can someone working in the area of several complex variables explain the geometric idea behind the Catlin multitype. I have seen the technical definition, but unable to grasp the idea behind this.
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2
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70
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Regular exposable points on the boundary of compacts in Stein manifolds
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 ...
- 779
2
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75
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Notation and geometry facts in a paper on the Diederich-Fornæss index
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 ...
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1
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55
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References for the generalized Dirichlet problem for plurisubharmonic functions on the bidisc
In the paper "On a Generalized Dirichlet Problem for Plurisubharmonic Functions and Pseudo-Convex Domains. Characterization of Silov Boundaries" Theorem 5.3, the following result is obtained ...
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1
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36
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Precise definition of locally closed complex curve
In Stein Manifold and Holomorphic Mappings, by Forstnerič, I refer to Definition 8.9.9:
An exposed point is a point belonging to a certain subset $\Sigma$ of $\Bbb C^2$, enjoying certain properties.
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1
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61
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Holomorphic dynamical systems defined on a contractible bounded open subset of $\Bbb{C}^n$
Let $U$ be a contractible bounded open subset of $\Bbb{C}$. There is a standard classification of possible dynamical behaviors of holomorphic maps $f:U\rightarrow U$:
Attracting Case: There is an ...
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1
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294
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Can an entire function have every root function?
My question is an amalgamation of two previous questions. The first question I'd like to draw attention to is here. It asks whether there can exist a non trivial semigroup defined on $\mathbb{C}$
$$\...
user78249
0
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122
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How to solve $\sqrt{-1}\partial\bar{\partial}u=\omega$
I'm looking for references on the study of the equation $\sqrt{-1}\partial\bar{\partial}u=\omega$,especially when $\omega$ is a k\"ahler metric on $\Omega\setminus S$,where $\Omega\subset \mathbb{C}^n$...
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