Mathematical Sciences: Isoperimetric Inequalities

首席研究员将继续他对几何凸性的定量方面的研究。特别是，他将研究布鲁恩-明科夫斯基的混合体积理论，这是定量凸性的核心。该奖项将支持积分几何一般领域的研究。集合的几何结构通常可以通过将集合分解成切片来分析和描述。切片的几何形状通常相当简单，很容易描述。分析中的主要困难通常是从切片的几何形状重建整个集合的基本几何特征。这一数学领域的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.