Isometric Rigidity of the Wasserstein Space W1(G) Over Carnot Groups

Balogh, Zoltán M. and Titkos, Tamás and Virosztek, Dániel (2026) Isometric Rigidity of the Wasserstein Space W1(G) Over Carnot Groups. POTENTIAL ANALYSIS, 64 (1). ISSN 0926-2601

Preview

Text 2305.05492v2.pdf - Draft Version Download (490kB) | Preview

Abstract

This paper aims to study isometries of the 1-Wasserstein space W1(G) over Carnot groups endowed with horizontally strictly convex norms. Well-known examples of horizontally strictly convex norms on Carnot groups are the Heisenberg group Hn endowed with the Heisenberg-Korányi norm, or with the Naor-Lee norm; and H-type Iwasawa groups endowed with a Korányi-type norm. We prove that on a general Carnot group there always exists a horizontally strictly convex norm. The main result of the paper says that if (G,NG) is a Carnot group where NG is a horizontally strictly convex norm on G, then the Wasserstein space W1(G) is isometrically rigid. That is, for every isometry Φ:W1(G)→W1(G) there exists an isometry ψ:G→G such that Φ=ψ#. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.

Actions (login required)

Edit Item