---
res:
bibo_abstract:
- "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\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R)
is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid
if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove
that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval
[0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only
if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass,
and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R)).@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Gyorgy Pal
foaf_name: Geher, Gyorgy Pal
foaf_surname: Geher
- foaf_Person:
foaf_givenName: Tamas
foaf_name: Titkos, Tamas
foaf_surname: Titkos
- foaf_Person:
foaf_givenName: Daniel
foaf_name: Virosztek, Daniel
foaf_surname: Virosztek
foaf_workInfoHomepage: http://www.librecat.org/personId=48DB45DA-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1090/tran/8113
bibo_issue: '8'
bibo_volume: 373
dct_date: 2020^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/00029947
- http://id.crossref.org/issn/10886850
dct_language: eng
dct_publisher: American Mathematical Society@
dct_subject:
- Wasserstein space
- isometric embeddings
- isometric rigidity
- exotic isometry flow
dct_title: Isometric study of Wasserstein spaces - the real line@
...