2025/02/13 by Balogh, Zoltán M., Ströher, Eric, Titkos, Tamás +1
#46E27 #49Q22 #54E40 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)
paper · doi:10.48550/arxiv.2502.09364
In this paper, we study isometries of p-Wasserstein spaces. In our first result, for every complete and separable metric space X and for every p≥1, we construct a metric space Y such that X embeds isometrically into Y, and the p-Wasserstein space over Y admits mass-splitting isometries. Our second result is about embeddings into rigid constructions. We show that any complete and separable metric space X can be embedded isometrically into a metric space Y such that the 1-Wasserstein space is isometrically rigid.