论文标题
对数孔函数的仿射不变地图
Affine invariant maps for log-concave functions
论文作者
论文摘要
Grünbaum引入了仿射不变点和图的地图，以研究凸组的对称结构。我们将这些概念扩展到功能设置。该集合对称性的作用现在是通过函数的均匀性来扮演的。我们表明，在仿射不变点的示例中，是对数凸函数及其santaló点的经典重心。我们还表明，最近引入的浮动功能，John-和Löwner功能是仿射不变地图的示例。他们的中心为对数凸函数的仿射点提供了新的示例。
Affine invariant points and maps for sets were introduced by Grünbaum to study the symmetry structure of convex sets. We extend these notions to a functional setting. The role of symmetry of the set is now taken by evenness of the function. We show that among the examples for affine invariant points are the classical center of gravity of a log-concave function and its Santaló point. We also show that the recently introduced floating functions and the John- and Löwner functions are examples of affine invariant maps. Their centers provide new examples of affine invariant points for log-concave functions.
