Mathematical Sciences: Nonlinear Aspects of the Geometry of Convex Sets

首席研究员将继续他的工作， 凸集几何及其相关的一些非线性问题 与几何学。这项研究的一个主要动机是 用于发展平移积分几何的公式。 这项研究将涉及研究某些新发现的 与混合体积有关的泛函。 该奖项将支持一般领域的研究， 积分几何通常可以分析集合的几何 并通过将集合分解为切片来描述。的 切片的几何形状通常相当简单， 形容分析的主要困难通常是 重建的基本几何特征的整个 从切片的几何形状设置。一个众所周知的应用 这个数学领域就是CAT扫描。

The principal investigator will continue his work on the geometry of convex sets and on some nonlinear problems associated with the geometry. A major motivation for the research is a need for the development of formulas of translative integral geometry. The research will involve the study of certain newly discovered functionals which are related to mixed volumes. This award will support research in the general area of integral geometry. The geometry of a set may often be analyzed and described by a decomposition of the set into slices. The geometry of the slices is often fairly simple and easy to describe. The main difficulty in the analysis is usually the reconstruction of the underlying geometric features of the entire set from the geometry of the slices. One well know application of this area of mathematics is the CAT scan.