本项目基于Bo"ro"czky等人2012年、Gardner等人2013年的最新成果与申请者前2个基金项目的方法、技巧和知识积累及近期观察，综合运用各种投影、对称、重排和摄动等几何方法与测度迁移、泛函算子变分和偏微分方程等分析方法，对一般测度的Orlicz Minkowski问题与对数Minkowski问题；与凸体或紧集M组合、Orlicz组合相联系的Brunn-Minkowski型极值问题；Orlicz迷向体迷向常数上界问题；信息论中矩熵不等式、Stam不等式和Cramer-Rao不等式的Orlicz形式以及Orlicz赋值理论在联盟博弈Shapley值中的应用等课题展开研究。旨在推进Orlicz-Brunn-Minkowski 理论中若干极值问题的研究或攻克1-2个重要问题，为其在有关数学领域及计算机高效能算法、机器人探索、医学CT理论、信息论和联盟博弈中的应用提供一定的理论与方法。

Based on the latest study achievements of Bo "ro" czky et al in 2012 and Gardner et al in 2013, the accumulation of methods,skills and knowledge in previous two foundation projects and the recently observiation of the applicant, the goal of this project is to use of a variety of projection, symmetrization, rearrangement and perturbation and etc geometric methods, to use the theory of mass transport, functional operators variational and partial differential equations and etc analysis methods, to study the Orlicz Minkowski problem and the Log-Minkowski problem for general measures; the Minkowski types extremal problems with associated convex bodies or compact sets M-combination or M-addition, Orlicz-combination or Orlicz- addition; the Orlicz isotropic bodies and ones isotropic constant upper bound problem; internal relations the moment entropy inequality, the Stam inequality and the Cramer-Rao inequality in the form of Orlicz in the information theory, assignment Shapley value in cooperative game theory and the valuation theory. The objective of this project is to move forward the study of certain extremal problems in the Orlicz- Brunn-Minkowski theory or overcome a 1-2 important issues, to provide the theoretical foundaton and `tools to its applications in other areas of mathematics and computer high-effect algorithms, robotic exploration, and medical CT theory, the information theory and the cooperative game theory.