论文标题
Moser-Trudinger不平等和复杂的Monge-Ampere方程
Moser-Trudinger inequalities and complex Monge-Ampere equation
论文作者
论文摘要
我们的目的是在复杂的几何形状的环境下给出Moser-trudinger不平等的版本。作为一个非常特殊的情况，我们的结果已经给出了新的Moser-trudinger不等式，以换取$ r^2 $中一个域的sobolev space $ w^{1,2} $。我们还推导了一个新的必要条件，用于在紧凑的卡勒歧管上给定的措施的复杂蒙格 - 安培方程，以接纳持有人连续解决方案。
Our aim is to give a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, our result already gives a new Moser-Trudinger inequality for functions in the Sobolev space $W^{1,2}$ of a domain in $R^2$. We also deduce a new necessary condition for the complex Monge-Ampere equation for a given measure on a compact Kahler manifold to admit a Holder continuous solution.
