Mathematical Sciences: Isoperimetric Inequalities

首席研究员将继续研究 几何凸性的定量方面。特别是他 我将研究Brunn-Minkowski混合体积理论， 数量凸性的核心。 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 是CAT扫描

The principal investigator will continue his research on the quantitative aspects of geometric convexity. In particular he will study the Brunn-Minkowski theory of mixed volumes which is at the core of quantitative convexity. 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 known application of this area of mathematics is the CAT scan.