Mathematical Sciences: Isoperimetric Inequalities

数学科学：等周不等式

• 批准号: 9507988
• 负责人: Erwin Lutwak
• 金额: $ 9.08万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9507988&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Isoperimetric; Inequalities

9507988 Lutwak The proposed research lies in the area of geometric convexity; more specifically, it focuses on the Brunn-Minkowski theory, otherwise known as the theory of mixed volumes. Various problems concerning convex bodies in space are proposed: the Minkowski problem, affine isoperimetric inequalities, and possible duals to the Brunn-Minkowski theory (replacing projections by intersections) are considered. The theory of mixed volumes has already found a wide variety of applications. In probability and statistics, it is used to supplement the Monte Carlo method. In geometric tomography, the theory is applied to various imaging (X-rays, and MRI scanners in particular) problems . One of the basic problems in the theory is the reconstruction of a convex body from a minimal set of its cross sections or projections.

小行星9507988 拟议的研究在于几何凸性领域;更具体地说，它侧重于Brunn-Minkowski理论，也称为混合体积理论。提出了关于凸体在空间中的各种问题：闵可夫斯基问题，仿射等周不等式，并考虑可能的破坏Brunn-Minkowski理论（取代投影的交叉点）。 混合体积理论已经得到了广泛的应用。在概率论和统计学中，它被用来补充蒙特卡罗方法。在几何层析成像中，该理论被应用于各种成像（特别是X射线和MRI扫描仪）问题。该理论的基本问题之一是从凸体的最小截面集或投影集重建凸体。