We study the structure of isometries of the quadratic Wasserstein space W2(Sn, · )over the sphere endowed with the distance inherited from the norm of Rn+1. We prove that W2(Sn, · )is isometrically rigid, meaning that its isometry group is isomorphic to that of (Sn, · ). This is in striking...

We describe surjective linear isometries and linear isometry groups of a large class of Lipschitz‐free spaces that includes, for example, Lipschitz‐free spaces over any graph. We define the notion of a Lipschitz‐free rigid metric space whose Lipschitz‐free space only admits surjective...

Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels, and they are conjectured to be genuine metrics on quantum state spaces by De Palma and Trevisan. We prove triangle inequality for quantum Wasserstein divergences for every quantum system...