2024/11/11 by Balogh, Zoltán M., Kiss, Gergely, Titkos, Tamás +1 · 1 citation
#46E27. Secondary: 60B05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Primary: 54E40
paper · doi:10.48550/arxiv.2411.07051
We study p-Wasserstein spaces over the branching spaces ℝ2 and [-1,1]2 equipped with the maximum norm metric. We show that these spaces are isometrically rigid for all p≥1, meaning that all isometries of these spaces are induced by isometries of the underlying space via the push-forward operation. This is in contrast to the case of the Euclidean metric since with that distance the 2-Wasserstein space over ℝ2 is not rigid. Also, we highlight that the 1-Wasserstein space is not rigid over the closed interval [-1,1], while according to our result, its two-dimensional analog, the closed unit ball [-1,1]2 with the more complicated geodesic structure is rigid.