Isometric rigidity of Wasserstein spaces: The graph metric case
Copyright policy )Isometric rigidity of Wasserstein spaces: The graph metric case
The aim of this paper is to prove that the p p -Wasserstein space W p ( X ) \mathcal {W}_p(X) is isometrically rigid for all p ≥ 1 p\geq 1 whenever X X is a countable graph metric space. As a consequence, we obtain that for every countable group H {H} and any p ≥ 1 p\geq 1 there exists a p p -Wasserstein space whose isometry group is isomorphic to H {H} .
QA Mathematics / matematika, isometric rigidity, Distance in graphs, 54E40, 46E27 (Primary), 54E70, 05C12 (Secondary), graph metric space, Metric Geometry (math.MG), Wasserstein space, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, isometry, Probabilistic metric spaces, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Special maps on metric spaces, Spaces of measures
QA Mathematics / matematika, isometric rigidity, Distance in graphs, 54E40, 46E27 (Primary), 54E70, 05C12 (Secondary), graph metric space, Metric Geometry (math.MG), Wasserstein space, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, isometry, Probabilistic metric spaces, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Special maps on metric spaces, Spaces of measures
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