1 citations · 1 across the 7 of their papers we have counts for
7 papers
Sharp Poincaré interpolation along Wasserstein geodesics
Bang-Xian Han, Zhuo-Nan Zhu
Let and be - and -strongly log-concave probability measures on , and let be their quadratic Wasserstein geodesic. We prove the sharp…
Contracting Transport Maps on Riemannian Manifolds
Shrey Aryan, Bang-Xian Han, Zhuo-Nan Zhu
We use inverse mean curvature flow to construct bi-Lipschitz maps that preserve normalized volume and decrease distances. These maps send a round sphere onto any smooth closed stri…
Two-mode stability for multi-marginal optimal transport maps
Bang-Xian Han, Zhuo-Nan Zhu
We establish a two-mode stability theory for Monge solutions of the multi-marginal optimal transport problem with barycentric quadratic cost. The associated tuple of maps splits in…
Quantitative Stability of Wasserstein Barycenters over Alexandrov Spaces with Lower Curvature Bounds
Bang-Xian Han, Zhuo-Nan Zhu
We prove quantitative stability estimates for Wasserstein barycenters on Alexandrov spaces with curvature bounded from below. The proof combines the variational strategy of Carlier…
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…