2019/04/29 by Nhan‐Phu Chung, Chung, Nhan-Phu, Thanh‐Son Trinh +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1904.12461
openalex publication_date 2019/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, using ideas of Liero, Mielke and Savaré in [21], we establish a Kantorovich duality for generalized Wasserstein distances W1a,b on a generalized Polish metric space, introduced by Picolli and Rossi. As a consequence, we give another proof that W1a,b coincide with flat metrics which is a main result of [25], and therefore we get a result of independent interest that (M(X), Wa,b1) is a geodesic space for every Polish metric space X. We also prove that (MG(X),Wpa,b) is isometric isomorphism to (M(X/G),Wpa,b) for isometric actions of a compact group G on a Polish metric space X; and several results of Gromov-Hausdorrf convergence and equivariant Gromov-Hausdorff convergence of generalized Wasserstein spaces. The latter results were proved for standard Wasserstein spaces in [22],[14] and [8] respectively.