论文标题
Wasserstein空间之间的可区分地图
Differentiable maps between Wasserstein spaces
论文作者
论文摘要
对于平滑，连接和完整的riemannian歧管的瓦斯尔斯坦空间之间的地图，提出了一个可不同性的概念。由于瓦斯坦斯坦空间上的切线空间构建的性质，我们仅给出了全球可不同性的定义，即，没有先前的偶然性差异概念。但是，根据我们的定义，我们恢复了差异的预期属性。特别焦点是由基础歧管之间平滑地图引起的推动图映射的可不同性能，以及可微分图的凸混合，并具有明确的差分结构。
A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a global definition of differentiability, i.e. without a prior notion of pointwise differentiability. With our definition, however, we recover the expected properties of a differential. Special focus is being put on differentiability properties of pushforward maps induced by smooth maps between the underlying manifolds, and on convex mixing of differentiable maps, with an explicit construction of the differential.
