Mathematical Sciences: Integral Geometry and Related Topics in Geometric Analysis

数学科学：积分几何及几何分析中的相关主题

• 批准号: 8904174
• 负责人: Eric Grinberg
• 金额: $ 7.26万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8904174&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integral; Geometry; Related

The principal investigator will continue to investigate questions of integral geometry and related problems in geometric analysis. He will investigate Radon transformations along submanifolds of symmetric spaces, finite analogues of Radon transformations, and further geometric inequalities for convex bodies and the Busemann-Petty problem. In a separate vein, he will investigate group-invariant function theory on Hermitian symmetric domains. A microcomputer will be used to perform experiments in geometric inequalities for finite Radon transformations. Convex three dimensional polyhedra include the cube, pyramid, and other classic solids of Euclidean geometry. In the theory of integral geometry, one might compute the probability that an arbitrary line in three dimensional space intersects both the origin and one of these polyhedra. Using a computer to motivate his mode of attack, the principal investigator will solve deep generalizations of such problems.

主要研究者将继续研究几何分析中积分几何和相关问题的问题。 他将研究沿着对称空间的子延伸，ra的有限类似物以及凸体的进一步的几何不等式和Busemann-Petty问题的进一步的几何不等度。 在另一种方面，他将研究对遗传学对称领域的群体不变函数理论。 微型计算机将用于执行有限ra rantressions的几何不等式实验。 凸的三维多面体包括立方体，金字塔和其他欧几里得几何形状的经典固体。 在整体几何学理论中，可能会计算出三维空间中任意线与这些多面体之一相交的任意线相交的概率。 首席研究员使用计算机激励他的攻击方式，将解决此类问题的深刻概括。