Correction to "Monge-Ampere Equations, the Bergman Kernel, and Geometry of Pseudoconvex Domains"
Correction to "Monge-Ampere Equations, the Bergman Kernel, and Geometry of Pseudoconvex Domains"
复制标题
对“Monge-Ampere 方程、Bergman 核和伪凸域几何”的更正
DOI：
10.2307/1970961
复制
发表时间：
1976
影响因子：
4.9
通讯作者：
C. Fefferman
中科院分区：
文献类型：
--
作者：
C. Fefferman
当考虑到符号的变化时，第414页上的定积分7同样为零，从而使第414页上的论证无效。414和415用aD代替aDO，第五节的论点在明显的小变化下适用，并且类似于-f的定积分是非零的。从定义函数r = z1 + 1 Z22 + i（z1 - 1）z12开始，得到类似于[1]第五节中的公式：2 i =（112 r12 + 48 ir 4）-2 288 yr 4 208 r14 1568 yr 20
When one takes account of the sign change, the definite integral 7 on p. 414 vanishes identically, thus invalidating the arguments on pp. 414 and 415. With aD, substituted for aDO, the arguments of Section V apply with obvious small changes, and the definite integral analogous to -f is non-zero. Starting with the defining function r = z1 + 1 Z22 + i(z1 1)zl2, one obtains the following formulas, analogous to those in Section V of [1]: 2i = (112r12 + 48ir4)-2 288yr4 208r14 1568yr20