All Questions
Tagged with several-complex-variables potential-theory
7 questions
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Characterizing some similarity invariant homogeneous log-superharmonic functions of matrices
Let $L:M_n(\mathbb{C})^r\rightarrow[0,\infty)$ be a function that satisfies the following properties:
$\log(L)$ is plurisubharmonic.
$L$ is homogeneous in the sense that $L(\lambda A_1,\dots,\lambda ...
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A characterization of plurisubharmonic functions
Let $\Omega\subset \mathbb{C}^n$ be an open subset. Let $u\colon \Omega\to [-\infty,+\infty)$ be an upper semi-continuous function.
Recall that $u$ is called plurisubharmonic (psh) if its restriction ...
- 21.8k
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When a strictly positive log pluriharmonic function $g$ is equal to the norm of holomorphic function?
Suppose $V$ is a local analytic variety (singular). Suppose $g$ a strictly positive log pluriharmonic function on $V$, i.e. $\log g$ is pluriharmonic. I wonder when $g=|f|^2$, where $f$ is a ...
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On the definition of Cauchy transform [closed]
I have seen two different definitions of the Cauchy transform of a smooth function one is with respect to the line integral (for eg. in. the book "The Cauchy transform and potential theory")...
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A question on the proof of Bedford-Taylor theorem in Demailly's book
I am trying to understand a proof of the Bedford-Taylor theorem on the weak convergence of Monge-Ampere operators of decreasing sequences of plurisubharmonic functions.
I am reading a proof in the ...
- 21.8k
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Restricted Perron-Bremermann envelopes
Consider an upper semicontinuous function $\phi: \Omega \to (-\infty, \infty]$, in the sense that $\phi = \phi^*$, where $\phi^*$ denotes the upper semicontinuous regularization
$$
\phi^*(z) = \...
- 151
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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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