Mathematical Sciences: Isoperimetric Inequalities

数学科学：等周不等式

• 批准号: 8902550
• 负责人: Erwin Lutwak
• 金额: $ 7.8万
• 依托单位: Polytechnic University of New York
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902550&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Isoperimetric; Inequalities

The principal investigator will solve a number of problems in the area of isometric inequalities. These involve generalized convex hypersurfaces, inequalities for affine surface area, intersection and projection problems, and the dual Brunn- Minkowski theory. Generalized convex bodies are related to convex bodies in the way generalized functions (distributions) are related to ordinary functions. Their utilization will enable the principal investigator to establish a number of conjectured affine isometric inequalities. The classical Brunn-Minkowski theory is ideal for handling questions involving projections of convex shapes. The slow progress on a number of important questions is due to the fact that this theory is unsuited for dealing with intersection problems. The principal investigator will use a dual Brunn- Minkowski theory to overcome these difficulties. This work has applications outside mathematics to such fields as stereology.

首席研究员将解决一系列问题 在等距不等式领域。 这些涉及广义 凸超曲面，仿射表面积的不等式， 交叉和投影问题，以及对偶布伦- 闵可夫斯基理论 广义凸体与 凸体的方式广义函数（分布） 与普通功能有关。 它们的使用将使 主要研究者建立了一些 仿射等距不等式 经典的Brunn-Minkowski理论是处理 涉及凸形投影的问题。 缓慢 在一些重要问题上取得进展是因为 这个理论不适合处理交叉点 问题 主要研究者将使用双布伦- 闵可夫斯基理论克服了这些困难。这项工作 数学之外的应用，如立体学。