# Tagged Questions

**2**

votes

**1**answer

284 views

### Variant of the Riemann Mapping Theorem for $Conf(\mathbb H^2)$?

According to the Riemann mapping theorem it is possible to map a simply connected open subset $B \subset \mathbb C$ into any other $B' \subset \mathbb C$ by a (bi-)holomorphic mapping. Moreover, such ...

**4**

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**1**answer

239 views

### infimum of the Calabi energy in a given Kahler class

Given a compact Kahler manifold $M^n$ and a Kahler class $\Omega$. We have the Calabi energy (or Calabi functional)
$$\textrm{Ca}(\omega)=\int_Ms^2(\omega)\omega^n,\qquad \forall \omega\in\Omega.$$
...

**0**

votes

**1**answer

193 views

### A question on the area of the unit disc w.r.t. a complete conformal metric

Question: Let $\Delta$ be the unit disc in $\mathbb{C}$ and $\rho(z)|dz|^2$ be a complete conformal metric on $\Delta$ where $\rho(z)$ is continuous on $\Delta$. Let $a$ be the infimum of $p ...

**4**

votes

**1**answer

332 views

### Characterization of the moduli space of the pair of pants in terms of the modules of the extremal ring domains

Hi, I was thinking about the following question ; I will appreciate it if somebody can give me a full or partial answer or can at least cite any reference(s)/ papers etc :
By $ \bar{P} $ , we ...

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vote

**1**answer

220 views

### Conformal Extension from a closed set to open

Let $Q = \{(x,y): x,y\geq 0\} $ be the 1st quadrant of $\mathbb R^2$, and $f$ is a function defined on it such that all the partial derivative(any order) of $f$ exists and continuous. By Whitney ...

**1**

vote

**0**answers

214 views

### glue together a sequence of holomorphic forms

hallo,
my problem is the following: i have a finite sequence of holomorphic $k-$forms $\alpha_{k}$, each defined on open subsets $U_{k} \subset M$, where $M$ is a complex $n$-dimensional manifold, ...

**0**

votes

**1**answer

268 views

### hesse matrix under diffeomorphism

Let $u : U \rightarrow \mathbb{R}$, where $U \subset \mathbb{C}^{n}$ be a strictly plurisubharmonic smooth function and consider its complex hesse matrix $Hess^{\mathbb{C}}(u)$. Furthermore consider a ...

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vote

**3**answers

752 views

### A simple ordinary differential equation

Consider an entire function $f : \mathbb{C} \rightarrow \mathbb{C}$! We search the function
$$ g: (a,b) \rightarrow \mathbb{C},$$ which solves the following equation locally: $g'(t)=f(g(t))$ and ...

**2**

votes

**1**answer

262 views

### Is the closure of an open holomorphically convex subset of a Stein space holomorphically convex?

Let X be a Stein manifold and U an open, connected, relatively compact, holomorphically convex subset of X. Is the closure of U in X holomorphically convex?
Also, if X is a Stein space with a finite ...

**4**

votes

**3**answers

1k views

### Most important domains, extension theorems, and functions in several complex variables

For a new learner of several complex variables, the many domains (eg holomorphically convex, pseduconvex, Stein) and the many extension theorems (eg Riemann) and the many functions (plurisubharmonic) ...