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math.MG2009★ 5 cited
Ramified optimal transportation in geodesic metric spaces
Qinglan Xia
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching str…
math.OC2009★ 12 cited
On the transport dimension of measures
Qinglan Xia, Anna Vershynina
In this article, we define the transport dimension of probability measures on using ramified optimal transportation theory. We show that the transport dimension of a…