2024/10/18 by Che, Mauricio, Galaz-García, Fernando, Kerin, Martin +1 · 2 citations
#53C21 #53C23 #58B20 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2410.14648
In this paper we study the isometric rigidity of certain classes of metric spaces with respect to the p-Wasserstein space. We prove that spaces that split a separable Hilbert space are not isometrically rigid with respect to ℙ2. We then prove that infinite rays are isometrically rigid with respect to ℙp for any p≥ 1, whereas taking infinite half-cylinders (i.e. product spaces of the form X× [0,∞)) over compact non-branching geodesic spaces preserves isometric rigidity with respect to ℙp, for p>1. Finally, we prove that spherical suspensions over compact spaces with diameter less than π/2 are isometrically rigid with respect to ℙp, for p>1.