In this paper, we first propose and establish an Orlicz log-Minkowski inequality for affine surface areas by introducing new concepts of affine surface area measures and using the newly established Orlicz Minkowski inequality for mixed affine surface areas. The new Orlicz log-Minkowski inequality in special cases yields the classical Minkowski inequality for mixed affine surface areas, areas log-Minkowki inequality \(L_{p}\) log-Minkowski inequality for affine surface areas and other log-Minkowski type inequalities for affine surface areas.

中文翻译：

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面积log-Minkowski不等式

在本文中，我们首先通过引入仿射表面积测量的新概念并使用新建立的混合仿射表面积的 Orlicz Minkowski 不等式，提出并建立仿射表面积的 Orlicz log-Minkowski 不等式。特殊情况下的新 Orlicz log-Minkowski 不等式产生混合仿射表面积的经典 Minkowski 不等式、仿射表面积的面积 log-Minkowski 不等式\(L_{p}\) log-Minkowski 不等式和其他 log-Minkowski 类型的不等式仿射表面积。