4 papers · 1 filter
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…
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…
Maz'ya-Shaposhnikova meet Bishop-Gromov
Bang-Xian Han, Andrea Pinamonti, Zhefeng Xu +1
We find a surprising link between Maz'ya-Shaposhnikova's well-known asymptotic formula concerning fractional Sobolev seminorms and the generalized Bishop-Gromov inequality. In the…
Sharp uncertainty principles on metric measure spaces
Bang-Xian Han, Zhefeng Xu
We study the Heisenberg-Pauli-Weyl uncertainty principle and the Caffarelli-Kohn-Nirenberg interpolation inequalities, on metric measure spaces satisfying measure contraction prope…