摘要
Busemann-Petty问题是凸几何及其相关学科中的一个极其重要的问题.在近几十年解决这一问题的过程中,凸几何学的研究领域和研究方法得到了极大的丰富和发展.本文首先阐述了Busemann-Petty问题的历史,然后综述了与Busemann-Petty问题紧密相关的一些公开问题和重要课题的研究现状和最新的进展.
Busemann-Petty problem is an important problem in Convex Geometry and its related subjects. The research area and approach of convex geometry have been enlarged and developed essentially during recent decades, in which the Busemann-Petty problem was solved completely. In this paper, we firstly recall the history of the Busemann-Petty problem, and then we give an overview of some famous open problems and some important topics associated closely to the Busemann-Petty problem. The new progress on these open problems and related topics are also presented in this survey paper.
出处
《数学进展》
CSCD
北大核心
2008年第5期513-526,共14页
Advances in Mathematics(China)
基金
国家自然科学基金(No.10671117).