本项目是2019年天元专项资助的连续申请，计划用三到五年甚至更长的时间，瞄准Minkowski问题相关重大问题，以"学研"为出发点,在打好凸几何分析、Monge-Ampere方程理论、最优输运基础的同时向团队青年教师和研究生介绍Minkowski问题相关热门问题并就关键性公开问题展开研究。2020年我们着重关注于Lp-Brunn-Minkowski不等式、最优运输问题及其实际应用等问题的研究力争部分解决Lp-MinKowski问题在p<1时的唯一性结果。继续加强研讨成员和博士研究生掌握相关研究涉及的重大问题、方法以及国际上该领域研究的一些最新进展，特别是研究Minkowski问题与Monge-Ampere方程的基本手方法和理论。推动湖南大学“偏微分方程与几何分析”团队的发展，加深国际同行特别是青年科研人员在该领域的合作研究。

This project is a continuous application for Tianyuan Special Fund in 2019. It is planned to take three to five years or more, to focus on the major issues related to Minkowski problem. Starting from "learning and research", this project will introduce the hot issues related to Minkowski problem to young teachers and graduate students of the team and make open problems while laying a good foundation for convex geometry analysis, Monge-Ampere equations and optimal transportation. In 2020, we focused on Lp-Brunn-Minkowski inequality, optimal transportation problem and its application, and strived to partially solve the uniqueness of Lp-Minkowski problem at p<1. We will continue to strengthen the group to grasp the major issues and methods involved in the relevant research, as well as some recent developments in this field in the world, especially the basic methods and theories of the Minkowski problem and the Monge-Ampere equations. It will promote the development of the team of "Partial Differential Equations and Geometric Analysis" of Hunan University, and deepen the cooperation of international colleagues, especially young researchers in this field.