10.1090/tran/8113
Geher, Gyorgy Pal
Gyorgy Pal
Geher
Titkos, Tamas
Tamas
Titkos
Virosztek, Daniel
Daniel
Virosztek
Isometric study of Wasserstein spaces - the real line
American Mathematical Society
2020
2020-01-29T10:20:46Z
2020-07-27T14:41:06Z
journal_article
https://research-explorer.app.ist.ac.at/record/7389
https://research-explorer.app.ist.ac.at/record/7389.json
00029947
2002.00859
Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space
W_p(R) for all p \in [1,\infty) \setminus {2}. We show that W_2(R) is also exceptional regarding the
parameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying
space, we prove that the exceptionality of p = 2 disappears if we replace R by the compact
interval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if
p is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))
cannot be embedded into Isom(W_1(R)).