迷向面积测度与凸体的投影

Isotropic Surface Area Measure and Projection of Convex Bodies

凸体的迷向面积测度与其投影的极值问题密切相关.首先讨论两个凸体具有迷向面积测度时,其Blaschke和的投影问题;然后就凸体的面积测度迷向时,讨论Schneider投影问题,并得到它与极小表面积的一个关系.

In this paper, projection of Blaschke sum of two convex bodies is considered when these convex bodies have an isotropic surface measure. The Schneider projection problem is also discussed when the convex body has an isotropic surface measure.