7 papers
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…
Stability of optimal transport on metric measure spaces
Bang-Xian Han, Zhuo-Nan Zhu
We prove a quantitative stability of Kantorovich potentials on metric measure spaces with lower Ricci curvature bound, thereby confirming a recent conjecture of Kitagawa, Letrouit…
On the Structure of Busemann Spaces with Non-Negative Curvature
Bang-Xian Han, Liming Yin
We extend the structure theory of Burago--Gromov--Perelman for Alexandrov spaces with curvature bounded below, to the setting of Busemann spaces with non-negative curvature. We pro…
A new characterization of Sobolev spaces on Lipschitz differentiability spaces
Bang-Xian Han, Zhe-Feng Xu, Zhuo-Nan Zhu
Numerous characterizations of Sobolev norms via the asymptotic behavior of non-local functionals have been established over the past decades; however, their validity beyond the PI…
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…