The main purpose of the present article is to introduce a new concept and call it Orlicz mixed geominimal surface area \(G_{\varphi }(K_{1},\ldots ,K_{n})\) of n convex bodies \(K_{1},\ldots ,K_{n}\), which obeys classical basic properties. The new affine geometric quantity in special case yields Petty’s geominimal surface area G(K), Lutwak’s p-geominimal surface area \(G_{p}(K)\) and the newly established Orlicz geominimal surface area \(G_{\varphi }(K)\). The Orlicz mixed geominimal surface area inequality is established, which in special case yields Petty’s geominimal surface area inequality, Lutwak’s p-geominimal surface area inequality and Orlicz geominimal surface area inequality, respectively. Moreover, the related concepts and inequalities of \(L_{p}\)-mixed geominimal surface area are also derived here.

本文的主要目的是引入一个新概念，并将其称为Orlicz 混合几何最小表面积 \(G_{\varphi }(K_{1},\ldots ,K_{n})\) n个凸体\( K_{1},\ldots ,K_{n}\)，遵循经典的基本属性。特殊情况下的新仿射几何量产生 Petty 的几何最小表面积G ( K )、Lutwak 的p几何最小表面积\(G_{p}(K)\)和新建立的 Orlicz 几何最小表面积\(G_{\varphi } (K)\)。建立了Orlicz混合地物最小表面积不等式，在特殊情况下分别产生Petty的地物最小表面积不等式、Lutwak的p-地物最小表面积不等式和Orlicz地物最小表面积不等式。此外，还导出了\(L_{p}\)-混合几何最小表面积的相关概念和不等式。