中文摘要：

为了解决Logarithmic Minkowski问题,已对球面上的任意有限偶Borel测度引入了Logarithmic函数.考虑单位球面上旋转不变概率测度的Logarithmic函数,并考虑它的最小值问题.

英文摘要：

In order to solve the Logarithmic Minkowski problem,the Logarithmic functional of finite even Borel measure on sphere was introduced.In this paper,the Logarithmic functional of rotationally invariant probability measure on sphere has been discussed and the minimal Logarithmic function has been studied.