Isometric rigidity of Wasserstein tori and spheres

Isometric rigidity of Wasserstein tori and spheres

We prove isometric rigidity for p‐Wasserstein spaces over finite‐dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials.

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Veröffentlicht in:Mathematika 2023-01, Vol.69 (1), p.20-32
Hauptverfasser: Gehér, György Pál, Titkos, Tamás, Virosztek, Dániel
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove isometric rigidity for p‐Wasserstein spaces over finite‐dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials.
ISSN:0025-5793
2041-7942
DOI:10.1112/mtk.12174