1 citations · 1 across the 13 of their papers we have counts for
11 papers · 1 filter
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…
Lipschitz regularity of harmonic map heat flows from spaces into spaces
Bang-Xian Han, Hui-Chun Zhang, Xi-Ping Zhu
We prove positive-time regularity for harmonic map heat flows from finite-dimensional spaces into complete spaces, without assuming that eithe…
Heat Codimension and Scalar Curvature
Bang-Xian Han
Motivated by recent proofs of Gromov's codimension-two volume-growth conjecture, we propose a synthetic theory for scalar lower bound on metric measure Dirichlet spaces.
Weak Quadruple Comparison and Structure Theory Beyond Alexandrov Geometry
Bang-Xian Han, Liming Yin
We introduce a new four-point comparison principle, called the -weak quadruple condition, for non-Riemannian spaces with synthetic non-negative curvature. This con…
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…
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…
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 I
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…
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…
ABP estimate on metric measure spaces via optimal transport
Bang-Xian Han
By using optimal transport theory, we establish a sharp Alexandroff--Bakelman--Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bo…