论文标题
凸功能的平稳估值
Smooth valuations on convex functions
论文作者
论文摘要
我们使用与凸功能相关的差分周期中的差分形式的集成在有限值凸功能的空间上构建估值。我们描述了此过程的内核，并表明，这一平稳估值空间与凸功能上所有连续的双向译数不变估值的空间的相交在后者中是密集的。作为应用程序，我们获得了1-同质，连续的，双重跨性别不变的估值的描述，这些估值相对于在单位球体上的紧凑型亚组而言是不变的。
We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We describe the kernel of this procedure and show that the intersection of this space of smooth valuations with the space of all continuous dually epi-translation invariant valuations on convex functions is dense in the latter. As an application, we obtain a description of 1-homogeneous, continuous, dually epi-translation invariant valuations that are invariant with respect to a compact subgroup operating transitively on the unit sphere.
