Curvature measures of convex bodies
Curvature measures of convex bodies
复制标题
凸体的曲率测量
DOI：
10.1007/bf02413869
复制
发表时间：
1978
期刊：
影响因子：
--
通讯作者：
R. Schneider
中科院分区：
文献类型：
--
作者：
R. Schneider
摘要在凸体的特殊情况下，研究了Federer提出的关于正可及集的曲率度量。此限制会产生额外的结果。其中包括：(5.1)，m阶曲率测度的积分几何解释，表明它在某种意义上度量接触凸体的余维m+1的仿射子空间；(6.1)，类似于Hadwiger对凸体质量积分的刻画的曲率测度(线性组合)的公理刻画；(8.1)，确定m阶曲率测度的支撑性，证明它是凸体的m-骨架的闭包。此外，对于凸体的情况，我们给出了曲率度量的积分几何运动学公式的一个新的、较短的证明。
SummaryThe curvature measures, introduced by Federer for the sets of positive reach, are investigated in the special case of convex bodies. This restriction yields additional results. Among them are:(5.1), an integral-geometric interpretation of the curvature measure of order m, showing that it measures, in a certain sense, the affine subspaces of codimension m+1 which touch the convex body;(6.1), an axiomatic characterization of the (linear combinations of) curvature measures similar to Hadwiger's characterization of the quermassintegrals of convex bodies;(8.1), the determination of the support of the curvature measure of order m, which turns out to be the closure of the m-skeleton of the convex body. Moreover we give, for the case of convex bodies, a new and comparatively short proof of an integral-geometric kinematic formula for curvature measures.