1 citations · 1 across the 3 of their papers we have counts for
4 papers
On the Geometry of Wasserstein Barycenter II: Riemannian Rigidity, Essential Non-Branching, and Finsler Models
Bang-Xian Han, Deng-Yu Liu
Wasserstein barycenters provide a notion of weighted mean for probability measures on a metric space. We prove that the barycenter curvature-dimension condition is…
Wasserstein Barycenter Convexity Detects Hilbertian Geometry
Bang-Xian Han, Deng-Yu Liu
We prove that convexity of the Boltzmann entropy at Wasserstein barycenters is strong enough to distinguish Hilbert spaces from general Banach spaces. Thus Wasserstein barycenters…
Barycenter curvature-dimension condition for extended metric measure spaces
Bang-Xian Han, Deng-yu Liu, Zhuo-nan Zhu
In this survey, we introduce a new curvature-dimension condition for extended metric measure spaces, called Barycenter-Curvature Dimension condition BCD, from the perspective of Wa…
On the geometry of Wasserstein barycenter I
Bang-Xian Han, Deng-Yu Liu, Zhuo-Nan Zhu
We study the Wasserstein barycenter problem in the setting of non-compact, non-smooth extended metric measure spaces. We introduce a couple of new concepts and obtain the existence…