病媒措施的最优输运
Optimal transport of vector measures
摘要：
我们发展和研究了矢量措施的最优输运理论。我们解决了克拉塔格的一个猜想，即在总质量为零的欧几里得空间上给定一个向量测度，任何运输集的质量也为零。我们提供了一个反例的猜想。我们概括的康托洛维奇-鲁宾斯坦对偶的向量措施设置。利用推广，我们回答的猜想是肯定的，只要存在一个最优输运，其全变差的绝对连续的边缘。
英文摘要：
We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with total mass zero, the mass of any transport set is again zero. We provide a counterexample to the conjecture. We generalise the Kantorovich--Rubinstein duality to the vector measures setting. Employing the generalisation, we answer the conjecture in the affirmative provided there exists an optimal transport with absolutely continuous marginals of its total variation.
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