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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…
math.MG2024
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…