# Tagged Questions

**0**

votes

**0**answers

90 views

### The type of a Riemann surface arising from a polynomial vector field

Consider the planar polynomial vector field $$\begin{cases} \dot x=P(x,y)\\ \dot y=Q(x,y)\end{cases}$$
It defines a singular foliation on $\mathbb{C}P^{2}$. Assume that a complex leaf contains ...

**2**

votes

**3**answers

255 views

### Solutions of the $\overline{\partial}$ equation in the upper half-plane

I am looking for references on solutions of the $\overline{\partial}$ equation in the upper half-plane (with conditions on the boundary). But this subject is completely outside my area of expertise ...

**4**

votes

**0**answers

354 views

### A generalization of Liouville formula for the determinant of a system of ODE?

Let $\Phi(t)$ be an $n\times n$ complex matrix whose columns are (independent) solutions of the system of ordinary differential equations (ODE):
$\frac{d}{dt}y= A(t) y$, where $A(t)$ is a ...

**0**

votes

**0**answers

137 views

### monge ampere equation along totally real submanifolds

hi,
are there some references when solving the complex monge ampere equation along totally real submanifolds of some compact (with boundary or without) complex manifold. i know that there are a lot ...

**3**

votes

**2**answers

406 views

### calabi conjecture on compact manifolds

hi,
is the calabi conjencture formulated for compact manifolds with boundary ? or only for those without boundary ? excuse me if the question is too trivial but in my literature it isn't mentioned ...

**0**

votes

**0**answers

252 views

### $\partial \bar{\partial}$ on a complex manifold

hallo,
i have the following question: let $M$ be a complex $n-$dimensional manifold and $R \subset M$ be a totally real, compact, $n-$dimensional (real) manifold. let $\alpha$ be a smooth nonnegative ...

**2**

votes

**0**answers

294 views

### Boundary behavior of Kähler cone with curvature restriction

Let $(M,\omega)$ be a compact Kähler manifold. The boundary behavior of Kähler cone is very interesting; however,it's hard to understand.
A fundamental result is due to Demailly and Paun: they ...

**-3**

votes

**1**answer

955 views

### Kolodziej's acta paper “the complex monge-ampere equation”——a detailed ploblem [closed]

Recently,I am reading kolodziej's acta paper,there are some ditails that i do not know clearly.
In the top line of page 99,"it's no restriction to assume that for each s we have ...