A geometric study of Wasserstein spaces: isometric rigidity in negative curvature (Q2800172)
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scientific article; zbMATH DE number 6569168
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A geometric study of Wasserstein spaces: isometric rigidity in negative curvature |
scientific article; zbMATH DE number 6569168 |
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15 April 2016
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Wasserstein space
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Hadamard space
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optimal transportation
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isometries
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A geometric study of Wasserstein spaces: isometric rigidity in negative curvature (English)
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This article is one from a series of papers devoted to the geometric properties of Wasserstein spaces defined for Hadamard spaces.NEWLINENEWLINELet \(X\) be a geodesically complete and proper Hadamard space and \(\mathcal W_2(X)\) -- the space of all Borel probability measures (of finite second moment) on \(X\) equipped with the metric defined from the optimal transportation. In contrast to the main result of [the second author, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 9, No. 2, 297--323 (2010; Zbl 1218.53079)], the authors show that if \(X\) is negatively curved then each isometry of \(\mathcal W_2(X)\) is induced by the isometry of \(X\) (Theorem 1.1).
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