凸几何分析是20世纪末在经典Brunn-Minkowski理论的基础上发展起来的几何学与泛函分析相结合的一门交叉学科，其研究的核心内容是Brunn-Minkowski理论，此理论中的两个核心概念是：体积和加法。基于这两个重要的概念，其发展过程经历了经典Brunn-Minkowski理论、Lp Brunn-Minkowski理论和Orlicz Brunn-Minkowski理论等几个阶段，每一个阶段都伴随着相应的加法算子，即Minkowski加、Lp加(Firey加)和Orlicz加等算子。本项目的主要研究内容是：紧凸集上Minkowski加、Lp加(Firey加)和Orlicz加等算子特征性质的研究；Orlicz Brunn-Minkowski理论中Orlicz Brunn-Minkowski不等式和Orlicz Minkowski不等式等Orlicz型不等式的研究。

Convex geometric analysis is an interdisciplinary subject of the geometry and functional analysis which has developed on the basis of classical Brunn-Minkowski theory at the end of twentieth Century, and its core content is Brunn-Minkowski theory. Volume and addition are the two core concepts of Brunn-Minkowski theory. On the base of the two important concepts, during the development of Brunn-Minkowski theory, it has undergone three stages: classical Brunn-Minkowski theory, Lp Brunn-Minkowski theory and Orlicz Brunn-Minkowski theory. Accordingly, every stage has its own addition, say Minkowski addition, Lp addition (Firey addition) and Orlicz addition. This project mainly includes the following contents: the research of the characteristic properties of the operators, say Lp addition, M addition, Orlicz addition and Blaschke addition, in compact convex sets; the research of Orlicz-type inequalities such as Orlicz Brunn-Minkowski inequality and Orlicz Minkowski inequality in Orlicz Brunn-Minkowski theory.