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math.DG2026
Optimal Transport and the ABP Method in Higher Codimension
Bang-Xian Han, Zhe-Feng Xu
We prove an inverse optimal-transport principle for the ABP contact set of animmersed submanifold. A fixed function on the submanifold determines, for every probability density on…
math.MG2026
Rigidity and Quantitative Stability of the Sliced Wasserstein Deficit
Bang-Xian Han
The sliced Wasserstein distance compares high-dimensional probability measures by averaging one-dimensional optimal transport distances over linear projections. Althoug…
math.MG2026
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…