The first variation of the total mass of log-concave functions was studied by Colesanti and Fragalà, which includes the mixed volume of convex bodies. Using Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log-concave functions, and its related affine isoperimetric inequality is also established.

中文翻译：

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功能最小几何表面积及其相关的仿射等距不等式

对数凹函数总质量的第一个变化是由Colesanti和Fragalà研究的，其中包括凸体的混合体积。使用Colesanti和Fragalà的第一个变式，我们定义了对数凹函数的最小几何表面积，并建立了与之相关的仿射等距不等式。