Mathematical Sciences: Integral Geometry and Related Topics in Geometric Analysis

首席研究员将继续研究积分几何和几何分析中的相关问题。他将研究沿对称空间子流形的Radon变换，Radon变换的有限类似物，以及凸体的进一步几何不等式和Busemann-Petty问题。在另一方面，他将研究厄米对称域上的群不变函数理论。将使用微型计算机进行有限氡变换几何不等式的实验。凸三维多面体包括立方体、金字塔和欧几里得几何中的其他经典立体。在积分几何理论中，人们可以计算三维空间中任意一条线与原点和其中一个多面体相交的概率。使用计算机来激发他的攻击模式，首席研究员将解决这些问题的深刻概括。

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.