论文标题
福尔摩斯 - 汤普森边界区域的Santaló点
The Santaló point for the Holmes-Thompson boundary area
论文作者
论文摘要
我们探讨了凸出体中凸形体的霍尔姆斯 - 汤普森边界区域的Santaló点的概念。在规范为$ c^1 $的情况下，如果单位球和凸面重合的情况，我们证明存在和独特性。当规范空间具有光滑的曲线弯曲的单位球时，我们表现出一个双重santaló点，表示是双体的投射质心平均值。
We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is $C^1$, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit ball, we exhibit a dual Santaló point expressed as an average of centroids of projections of the dual body.
