1
vote
0answers
54 views

About the integral of the plurisubharmonic functions on the whole manifold

Let $(M,\omega)$ be a Kahler manifold with positive first Chern class. $\omega\in c_1(M)$ is a Kahler current. $D$ is a smooth simple divisor in $-K_M$. $s$ is a determining section of $D$. The ...
2
votes
3answers
229 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
0answers
342 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
0answers
132 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 ...
2
votes
2answers
395 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
0answers
243 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
0answers
285 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
1answer
942 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 ...