论文标题
在$ \ mathbb {c}^2 $中的pseudoconvex域的PseudoConvex域上的plurisubharmonic定义函数
On plurisubharmonic defining functions for pseudoconvex domains in $\mathbb{C}^2$
论文作者
论文摘要
我们研究了$ \ mathbb {c}^2 $中平滑界限的pseudoconvex域的plurisubharmonic定义函数的存在问题。特别是，我们构建了一个简单的反示例家族，以实现Plurisubharmonic平滑局部定义功能的存在。此外，我们给出了一般标准，等同于在域边界上或附近的plurisubharmonic平滑定义函数的存在。然后，针对某些类别的域进行了这些等效的特征。
We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of plurisubharmonic smooth local defining functions. Moreover, we give general criteria equivalent to the existence of plurisubharmonic smooth defining functions on or near the boundary of the domain. These equivalent characterizations are then explored for some classes of domains.
