Deng-yu Liu

activity

20242026

most citedOn the geometry of Wasserstein barycenter I

1 citations · 1 across the 3 of their papers we have counts for

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math.MG2026

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 $BCD (K, N)$ is…

math.MG2026

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…