Isometric rigidity of Wasserstein spaces: The graph metric case
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- by Gergely Kiss and Tamás Titkos
- Proc. Amer. Math. Soc. 150 (2022), 4083-4097
- DOI: https://doi.org/10.1090/proc/15977
- Published electronically: April 29, 2022
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Abstract:
The aim of this paper is to prove that the $p$-Wasserstein space $\mathcal {W}_p(X)$ is isometrically rigid for all $p\geq 1$ whenever $X$ is a countable graph metric space. As a consequence, we obtain that for every countable group ${H}$ and any $p\geq 1$ there exists a $p$-Wasserstein space whose isometry group is isomorphic to ${H}$.References
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Bibliographic Information
- Gergely Kiss
- Affiliation: Alfréd Rényi Institute of Mathematics – Eötvös Loránd Research Network, Reáltanoda u. 13–15, Budapest H-1053, Hungary
- MR Author ID: 924162
- Email: kiss.gergely@renyi.hu
- Tamás Titkos
- Affiliation: Alfréd Rényi Institute of Mathematics – Eötvös Loránd Research Network, Reáltanoda u. 13–15, Budapest H-1053, Hungary; and BBS University of Applied Sciences, Alkotmány u. 9, Budapest H-1054, Hungary
- Email: titkos.tamas@renyi.hu
- Received by editor(s): September 29, 2021
- Received by editor(s) in revised form: November 29, 2021
- Published electronically: April 29, 2022
- Additional Notes: The first author was supported by Premium Postdoctoral Fellowship of the Hungarian Academy of Sciences and by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K124749). The second author was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374 and grant no. K134944), by the János Bolyai Research Scholarship and the Momentum Program No. LP2021-15/2021 of the Hungarian Academy of Sciences, and by the ÚNKP-20-5-BGE-1 New National Excellence Program of the Ministry of Innovation and Technology.
The second author is the corresponding author. - Communicated by: Nageswari Shanmugalingam
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4083-4097
- MSC (2020): Primary 54E40, 46E27; Secondary 54E70, 05C12
- DOI: https://doi.org/10.1090/proc/15977
- MathSciNet review: 4446253