Orlicz–Brunn–Minkowski 理论是近几年兴起的一门以凸体和星体为主要研究对象的现代几何学，它是Lp-Brunn-Minkowski理论在Orlicz-空间的延伸和发展，有着广阔的研究前景。本项目运用实分析、泛函分析、微分几何、Lp-B-M理论及Banach空间几何学的渐近理论思想和方法，去研究Orlicz-空间几何体的若干典型问题。主要包括：1）Orlicz-空间几何体的极值和不等式问题；2）Orlicz-空间几何体的Shephard问题和Busemann-Petty问题；3）Orlicz-空间非对称体的定义和度量问题； 4）Orlicz-空间几何体的Orlicz-仿射表面积和Orlicz-几何表面积。这些研究不仅能丰富和发展Orlicz-Brunn-Minkowski理论，而且也可以使我们以更高、更统一的观点来看待凸几何问题。

The Orlicz-Brunn-Minkowski theory is a modern geometry rising in recent years, with convex body and stars body as the main research object, which is the extension and development of Lp-Brunn-Minkowski theory in Orlicz-space and has broad research prospects. The project will use the thought and method of real analysis, functional analysis, differential geometry, the Lp-B-M theory and the asymptotic theory of Banach space geometry, to study several typical problems of Orlicz-space geometry, which mainly includes: 1) the extreme value and inequality problems of Orlicz-space geometry body; 2) the Shephard problems and Busemann- Petty problems of Orlicz-space geometry body; 3) the definition and measurement problems of unsymmetrical body in Orlicz-space; 4) the Orlicz-affine surface area and Orlicz-geometric surface area of Orlicz-space geometry body. These studies not only can enrich and develop the Orlicz-Brunn-Minkowski theory, but also enables us to view the convex geometry problem with a higher and more unified perspective.